diff --git a/flang/runtime/matmul-transpose.cpp b/flang/runtime/matmul-transpose.cpp
--- a/flang/runtime/matmul-transpose.cpp
+++ b/flang/runtime/matmul-transpose.cpp
@@ -52,25 +52,64 @@
 //    DO 2 I = 1, NROWS
 //     DO 2 K = 1, N
 //   2  RES(I,J) = RES(I,J) + X(K,I)*Y(K,J) ! loop-invariant last term
-template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT,
+    bool X_HAS_STRIDED_COLUMNS, bool Y_HAS_STRIDED_COLUMNS>
 inline static void MatrixTransposedTimesMatrix(
     CppTypeFor<RCAT, RKIND> *RESTRICT product, SubscriptValue rows,
     SubscriptValue cols, const XT *RESTRICT x, const YT *RESTRICT y,
-    SubscriptValue n) {
+    SubscriptValue n, std::size_t xColumnByteStride = 0,
+    std::size_t yColumnByteStride = 0) {
   using ResultType = CppTypeFor<RCAT, RKIND>;
 
   std::memset(product, 0, rows * cols * sizeof *product);
   for (SubscriptValue j{0}; j < cols; ++j) {
     for (SubscriptValue i{0}; i < rows; ++i) {
       for (SubscriptValue k{0}; k < n; ++k) {
-        ResultType x_ki = static_cast<ResultType>(x[i * n + k]);
-        ResultType y_kj = static_cast<ResultType>(y[j * n + k]);
+        ResultType x_ki;
+        if constexpr (!X_HAS_STRIDED_COLUMNS) {
+          x_ki = static_cast<ResultType>(x[i * n + k]);
+        } else {
+          x_ki = static_cast<ResultType>(reinterpret_cast<const XT *>(
+              reinterpret_cast<const char *>(x) + i * xColumnByteStride)[k]);
+        }
+        ResultType y_kj;
+        if constexpr (!Y_HAS_STRIDED_COLUMNS) {
+          y_kj = static_cast<ResultType>(y[j * n + k]);
+        } else {
+          y_kj = static_cast<ResultType>(reinterpret_cast<const YT *>(
+              reinterpret_cast<const char *>(y) + j * yColumnByteStride)[k]);
+        }
         product[j * rows + i] += x_ki * y_kj;
       }
     }
   }
 }
 
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+inline static void MatrixTransposedTimesMatrixHelper(
+    CppTypeFor<RCAT, RKIND> *RESTRICT product, SubscriptValue rows,
+    SubscriptValue cols, const XT *RESTRICT x, const YT *RESTRICT y,
+    SubscriptValue n, std::optional<std::size_t> xColumnByteStride,
+    std::optional<std::size_t> yColumnByteStride) {
+  if (!xColumnByteStride) {
+    if (!yColumnByteStride) {
+      MatrixTransposedTimesMatrix<RCAT, RKIND, XT, YT, false, false>(
+          product, rows, cols, x, y, n);
+    } else {
+      MatrixTransposedTimesMatrix<RCAT, RKIND, XT, YT, false, true>(
+          product, rows, cols, x, y, n, 0, *yColumnByteStride);
+    }
+  } else {
+    if (!yColumnByteStride) {
+      MatrixTransposedTimesMatrix<RCAT, RKIND, XT, YT, true, false>(
+          product, rows, cols, x, y, n, *xColumnByteStride);
+    } else {
+      MatrixTransposedTimesMatrix<RCAT, RKIND, XT, YT, true, true>(
+          product, rows, cols, x, y, n, *xColumnByteStride, *yColumnByteStride);
+    }
+  }
+}
+
 // Contiguous numeric matrix*vector multiplication
 //   matrix(rows,n) * column vector(n) -> column vector(rows)
 // Straightforward algorithm:
@@ -85,21 +124,43 @@
 //   DO 2 I = 1, NROWS
 //    DO 2 K = 1, N
 //   2 RES(I) = RES(I) + X(K,I)*Y(K)
-template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT,
+    bool X_HAS_STRIDED_COLUMNS>
 inline static void MatrixTransposedTimesVector(
     CppTypeFor<RCAT, RKIND> *RESTRICT product, SubscriptValue rows,
-    SubscriptValue n, const XT *RESTRICT x, const YT *RESTRICT y) {
+    SubscriptValue n, const XT *RESTRICT x, const YT *RESTRICT y,
+    std::size_t xColumnByteStride = 0) {
   using ResultType = CppTypeFor<RCAT, RKIND>;
   std::memset(product, 0, rows * sizeof *product);
   for (SubscriptValue i{0}; i < rows; ++i) {
     for (SubscriptValue k{0}; k < n; ++k) {
-      ResultType x_ki = static_cast<ResultType>(x[i * n + k]);
+      ResultType x_ki;
+      if constexpr (!X_HAS_STRIDED_COLUMNS) {
+        x_ki = static_cast<ResultType>(x[i * n + k]);
+      } else {
+        x_ki = static_cast<ResultType>(reinterpret_cast<const XT *>(
+            reinterpret_cast<const char *>(x) + i * xColumnByteStride)[k]);
+      }
       ResultType y_k = static_cast<ResultType>(y[k]);
       product[i] += x_ki * y_k;
     }
   }
 }
 
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+inline static void MatrixTransposedTimesVectorHelper(
+    CppTypeFor<RCAT, RKIND> *RESTRICT product, SubscriptValue rows,
+    SubscriptValue n, const XT *RESTRICT x, const YT *RESTRICT y,
+    std::optional<std::size_t> xColumnByteStride) {
+  if (!xColumnByteStride) {
+    MatrixTransposedTimesVector<RCAT, RKIND, XT, YT, false>(
+        product, rows, n, x, y);
+  } else {
+    MatrixTransposedTimesVector<RCAT, RKIND, XT, YT, true>(
+        product, rows, n, x, y, *xColumnByteStride);
+  }
+}
+
 // Implements an instance of MATMUL for given argument types.
 template <bool IS_ALLOCATING, TypeCategory RCAT, int RKIND, typename XT,
     typename YT>
@@ -149,19 +210,39 @@
   const SubscriptValue rows{extent[0]};
   const SubscriptValue cols{extent[1]};
   if constexpr (RCAT != TypeCategory::Logical) {
-    if (x.IsContiguous() && y.IsContiguous() &&
+    if (x.IsContiguous(1) && y.IsContiguous(1) &&
         (IS_ALLOCATING || result.IsContiguous())) {
-      // Contiguous numeric matrices
+      // Contiguous numeric matrices (maybe with columns
+      // separated by a stride).
+      std::optional<std::size_t> xColumnByteStride;
+      if (!x.IsContiguous()) {
+        // X's columns are strided.
+        SubscriptValue xAt[2]{};
+        x.GetLowerBounds(xAt);
+        xAt[1]++;
+        xColumnByteStride = x.SubscriptsToByteOffset(xAt);
+      }
+      std::optional<std::size_t> yColumnByteStride;
+      if (!y.IsContiguous()) {
+        // Y's columns are strided.
+        SubscriptValue yAt[2]{};
+        y.GetLowerBounds(yAt);
+        yAt[1]++;
+        yColumnByteStride = y.SubscriptsToByteOffset(yAt);
+      }
       if (resRank == 2) { // M*M -> M
-        MatrixTransposedTimesMatrix<RCAT, RKIND, XT, YT>(
+        // TODO: use BLAS-3 GEMM for supported types.
+        MatrixTransposedTimesMatrixHelper<RCAT, RKIND, XT, YT>(
             result.template OffsetElement<WriteResult>(), rows, cols,
-            x.OffsetElement<XT>(), y.OffsetElement<YT>(), n);
+            x.OffsetElement<XT>(), y.OffsetElement<YT>(), n, xColumnByteStride,
+            yColumnByteStride);
         return;
       }
       if (xRank == 2) { // M*V -> V
-        MatrixTransposedTimesVector<RCAT, RKIND, XT, YT>(
+        // TODO: use BLAS-2 GEMM for supported types.
+        MatrixTransposedTimesVectorHelper<RCAT, RKIND, XT, YT>(
             result.template OffsetElement<WriteResult>(), rows, n,
-            x.OffsetElement<XT>(), y.OffsetElement<YT>());
+            x.OffsetElement<XT>(), y.OffsetElement<YT>(), xColumnByteStride);
         return;
       }
       // else V*M -> V (not allowed because TRANSPOSE() is only defined for rank
diff --git a/flang/runtime/matmul.cpp b/flang/runtime/matmul.cpp
--- a/flang/runtime/matmul.cpp
+++ b/flang/runtime/matmul.cpp
@@ -69,10 +69,12 @@
 //    DO 2 J = 1, NCOLS
 //     DO 2 I = 1, NROWS
 //   2  RES(I,J) = RES(I,J) + X(I,K)*Y(K,J) ! loop-invariant last term
-template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT,
+    bool X_HAS_STRIDED_COLUMNS, bool Y_HAS_STRIDED_COLUMNS>
 inline void MatrixTimesMatrix(CppTypeFor<RCAT, RKIND> *RESTRICT product,
     SubscriptValue rows, SubscriptValue cols, const XT *RESTRICT x,
-    const YT *RESTRICT y, SubscriptValue n) {
+    const YT *RESTRICT y, SubscriptValue n, std::size_t xColumnByteStride = 0,
+    std::size_t yColumnByteStride = 0) {
   using ResultType = CppTypeFor<RCAT, RKIND>;
   std::memset(product, 0, rows * cols * sizeof *product);
   const XT *RESTRICT xp0{x};
@@ -80,12 +82,48 @@
     ResultType *RESTRICT p{product};
     for (SubscriptValue j{0}; j < cols; ++j) {
       const XT *RESTRICT xp{xp0};
-      auto yv{static_cast<ResultType>(y[k + j * n])};
+      ResultType yv;
+      if constexpr (!Y_HAS_STRIDED_COLUMNS) {
+        yv = static_cast<ResultType>(y[k + j * n]);
+      } else {
+        yv = static_cast<ResultType>(reinterpret_cast<const YT *>(
+            reinterpret_cast<const char *>(y) + j * yColumnByteStride)[k]);
+      }
       for (SubscriptValue i{0}; i < rows; ++i) {
         *p++ += static_cast<ResultType>(*xp++) * yv;
       }
     }
-    xp0 += rows;
+    if constexpr (!X_HAS_STRIDED_COLUMNS) {
+      xp0 += rows;
+    } else {
+      xp0 = reinterpret_cast<const XT *>(
+          reinterpret_cast<const char *>(xp0) + xColumnByteStride);
+    }
+  }
+}
+
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+inline void MatrixTimesMatrixHelper(CppTypeFor<RCAT, RKIND> *RESTRICT product,
+    SubscriptValue rows, SubscriptValue cols, const XT *RESTRICT x,
+    const YT *RESTRICT y, SubscriptValue n,
+    std::optional<std::size_t> xColumnByteStride,
+    std::optional<std::size_t> yColumnByteStride) {
+  if (!xColumnByteStride) {
+    if (!yColumnByteStride) {
+      MatrixTimesMatrix<RCAT, RKIND, XT, YT, false, false>(
+          product, rows, cols, x, y, n);
+    } else {
+      MatrixTimesMatrix<RCAT, RKIND, XT, YT, false, true>(
+          product, rows, cols, x, y, n, 0, *yColumnByteStride);
+    }
+  } else {
+    if (!yColumnByteStride) {
+      MatrixTimesMatrix<RCAT, RKIND, XT, YT, true, false>(
+          product, rows, cols, x, y, n, *xColumnByteStride);
+    } else {
+      MatrixTimesMatrix<RCAT, RKIND, XT, YT, true, true>(
+          product, rows, cols, x, y, n, *xColumnByteStride, *yColumnByteStride);
+    }
   }
 }
 
@@ -103,18 +141,37 @@
 //   DO 2 K = 1, N
 //    DO 2 J = 1, NROWS
 //   2 RES(J) = RES(J) + X(J,K)*Y(K)
-template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT,
+    bool X_HAS_STRIDED_COLUMNS>
 inline void MatrixTimesVector(CppTypeFor<RCAT, RKIND> *RESTRICT product,
     SubscriptValue rows, SubscriptValue n, const XT *RESTRICT x,
-    const YT *RESTRICT y) {
+    const YT *RESTRICT y, std::size_t xColumnByteStride = 0) {
   using ResultType = CppTypeFor<RCAT, RKIND>;
   std::memset(product, 0, rows * sizeof *product);
+  [[maybe_unused]] const XT *RESTRICT xp0{x};
   for (SubscriptValue k{0}; k < n; ++k) {
     ResultType *RESTRICT p{product};
     auto yv{static_cast<ResultType>(*y++)};
     for (SubscriptValue j{0}; j < rows; ++j) {
       *p++ += static_cast<ResultType>(*x++) * yv;
     }
+    if constexpr (X_HAS_STRIDED_COLUMNS) {
+      xp0 = reinterpret_cast<const XT *>(
+          reinterpret_cast<const char *>(xp0) + xColumnByteStride);
+      x = xp0;
+    }
+  }
+}
+
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+inline void MatrixTimesVectorHelper(CppTypeFor<RCAT, RKIND> *RESTRICT product,
+    SubscriptValue rows, SubscriptValue n, const XT *RESTRICT x,
+    const YT *RESTRICT y, std::optional<std::size_t> xColumnByteStride) {
+  if (!xColumnByteStride) {
+    MatrixTimesVector<RCAT, RKIND, XT, YT, false>(product, rows, n, x, y);
+  } else {
+    MatrixTimesVector<RCAT, RKIND, XT, YT, true>(
+        product, rows, n, x, y, *xColumnByteStride);
   }
 }
 
@@ -132,10 +189,11 @@
 //   DO 2 K = 1, N
 //    DO 2 J = 1, NCOLS
 //   2 RES(J) = RES(J) + X(K)*Y(K,J)
-template <TypeCategory RCAT, int RKIND, typename XT, typename YT>
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT,
+    bool Y_HAS_STRIDED_COLUMNS>
 inline void VectorTimesMatrix(CppTypeFor<RCAT, RKIND> *RESTRICT product,
     SubscriptValue n, SubscriptValue cols, const XT *RESTRICT x,
-    const YT *RESTRICT y) {
+    const YT *RESTRICT y, std::size_t yColumnByteStride = 0) {
   using ResultType = CppTypeFor<RCAT, RKIND>;
   std::memset(product, 0, cols * sizeof *product);
   for (SubscriptValue k{0}; k < n; ++k) {
@@ -144,11 +202,29 @@
     const YT *RESTRICT yp{&y[k]};
     for (SubscriptValue j{0}; j < cols; ++j) {
       *p++ += xv * static_cast<ResultType>(*yp);
-      yp += n;
+      if constexpr (!Y_HAS_STRIDED_COLUMNS) {
+        yp += n;
+      } else {
+        yp = reinterpret_cast<const YT *>(
+            reinterpret_cast<const char *>(yp) + yColumnByteStride);
+      }
     }
   }
 }
 
+template <TypeCategory RCAT, int RKIND, typename XT, typename YT,
+    bool SPARSE_COLUMNS = false>
+inline void VectorTimesMatrixHelper(CppTypeFor<RCAT, RKIND> *RESTRICT product,
+    SubscriptValue n, SubscriptValue cols, const XT *RESTRICT x,
+    const YT *RESTRICT y, std::optional<std::size_t> yColumnByteStride) {
+  if (!yColumnByteStride) {
+    VectorTimesMatrix<RCAT, RKIND, XT, YT, false>(product, n, cols, x, y);
+  } else {
+    VectorTimesMatrix<RCAT, RKIND, XT, YT, true>(
+        product, n, cols, x, y, *yColumnByteStride);
+  }
+}
+
 // Implements an instance of MATMUL for given argument types.
 template <bool IS_ALLOCATING, TypeCategory RCAT, int RKIND, typename XT,
     typename YT>
@@ -194,13 +270,35 @@
       CppTypeFor<RCAT == TypeCategory::Logical ? TypeCategory::Integer : RCAT,
           RKIND>;
   if constexpr (RCAT != TypeCategory::Logical) {
-    if (x.IsContiguous() && y.IsContiguous() &&
+    if (x.IsContiguous(1) && y.IsContiguous(1) &&
         (IS_ALLOCATING || result.IsContiguous())) {
-      // Contiguous numeric matrices
+      // Contiguous numeric matrices (maybe with columns
+      // separated by a stride).
+      std::optional<std::size_t> xColumnByteStride;
+      if (!x.IsContiguous()) {
+        // X's columns are strided.
+        SubscriptValue xAt[2]{};
+        x.GetLowerBounds(xAt);
+        xAt[1]++;
+        xColumnByteStride = x.SubscriptsToByteOffset(xAt);
+      }
+      std::optional<std::size_t> yColumnByteStride;
+      if (!y.IsContiguous()) {
+        // Y's columns are strided.
+        SubscriptValue yAt[2]{};
+        y.GetLowerBounds(yAt);
+        yAt[1]++;
+        yColumnByteStride = y.SubscriptsToByteOffset(yAt);
+      }
+      // Note that BLAS GEMM can be used for the strided
+      // columns by setting proper leading dimension size.
+      // This implies that the column stride is divisible
+      // by the element size, which is usually true.
       if (resRank == 2) { // M*M -> M
         if (std::is_same_v<XT, YT>) {
           if constexpr (std::is_same_v<XT, float>) {
             // TODO: call BLAS-3 SGEMM
+            // TODO: try using CUTLASS for device.
           } else if constexpr (std::is_same_v<XT, double>) {
             // TODO: call BLAS-3 DGEMM
           } else if constexpr (std::is_same_v<XT, std::complex<float>>) {
@@ -209,9 +307,10 @@
             // TODO: call BLAS-3 ZGEMM
           }
         }
-        MatrixTimesMatrix<RCAT, RKIND, XT, YT>(
+        MatrixTimesMatrixHelper<RCAT, RKIND, XT, YT>(
             result.template OffsetElement<WriteResult>(), extent[0], extent[1],
-            x.OffsetElement<XT>(), y.OffsetElement<YT>(), n);
+            x.OffsetElement<XT>(), y.OffsetElement<YT>(), n, xColumnByteStride,
+            yColumnByteStride);
         return;
       } else if (xRank == 2) { // M*V -> V
         if (std::is_same_v<XT, YT>) {
@@ -225,9 +324,9 @@
             // TODO: call BLAS-2 ZGEMV(x,y)
           }
         }
-        MatrixTimesVector<RCAT, RKIND, XT, YT>(
+        MatrixTimesVectorHelper<RCAT, RKIND, XT, YT>(
             result.template OffsetElement<WriteResult>(), extent[0], n,
-            x.OffsetElement<XT>(), y.OffsetElement<YT>());
+            x.OffsetElement<XT>(), y.OffsetElement<YT>(), xColumnByteStride);
         return;
       } else { // V*M -> V
         if (std::is_same_v<XT, YT>) {
@@ -241,9 +340,9 @@
             // TODO: call BLAS-2 ZGEMV(y,x)
           }
         }
-        VectorTimesMatrix<RCAT, RKIND, XT, YT>(
+        VectorTimesMatrixHelper<RCAT, RKIND, XT, YT>(
             result.template OffsetElement<WriteResult>(), n, extent[0],
-            x.OffsetElement<XT>(), y.OffsetElement<YT>());
+            x.OffsetElement<XT>(), y.OffsetElement<YT>(), yColumnByteStride);
         return;
       }
     }
diff --git a/flang/unittests/Runtime/Matmul.cpp b/flang/unittests/Runtime/Matmul.cpp
--- a/flang/unittests/Runtime/Matmul.cpp
+++ b/flang/unittests/Runtime/Matmul.cpp
@@ -27,6 +27,16 @@
       std::vector<int>{3, 2}, std::vector<std::int16_t>{6, 7, 8, 9, 10, 11})};
   auto v{MakeArray<TypeCategory::Integer, 8>(
       std::vector<int>{2}, std::vector<std::int64_t>{-1, -2})};
+
+  // X2  0  2  4  Y2 -1 -1
+  //     1  3  5      6  9
+  //    -1 -1 -1      7 10
+  //                  8 11
+  auto x2{MakeArray<TypeCategory::Integer, 4>(std::vector<int>{3, 3},
+      std::vector<std::int32_t>{0, 1, -1, 2, 3, -1, 4, 5})};
+  auto y2{MakeArray<TypeCategory::Integer, 2>(std::vector<int>{4, 2},
+      std::vector<std::int16_t>{-1, 6, 7, 8, -1, 9, 10, 11})};
+
   StaticDescriptor<2, true> statDesc;
   Descriptor &result{statDesc.descriptor()};
 
@@ -73,6 +83,98 @@
   EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(2), -30);
   result.Destroy();
 
+  // Test non-contiguous sections.
+  static constexpr int sectionRank{2};
+  StaticDescriptor<sectionRank> sectionStaticDescriptorX2;
+  Descriptor &sectionX2{sectionStaticDescriptorX2.descriptor()};
+  sectionX2.Establish(x2->type(), x2->ElementBytes(),
+      /*p=*/nullptr, /*rank=*/sectionRank);
+  static const SubscriptValue lowersX2[]{1, 1}, uppersX2[]{2, 3};
+  // Section of X2:
+  //   +--------+
+  //   | 0  2  4|
+  //   | 1  3  5|
+  //   +--------+
+  //    -1 -1 -1
+  const auto errorX2{CFI_section(
+      &sectionX2.raw(), &x2->raw(), lowersX2, uppersX2, /*strides=*/nullptr)};
+  ASSERT_EQ(errorX2, 0) << "CFI_section failed for X2: " << errorX2;
+
+  StaticDescriptor<sectionRank> sectionStaticDescriptorY2;
+  Descriptor &sectionY2{sectionStaticDescriptorY2.descriptor()};
+  sectionY2.Establish(y2->type(), y2->ElementBytes(),
+      /*p=*/nullptr, /*rank=*/sectionRank);
+  static const SubscriptValue lowersY2[]{2, 1};
+  // Section of Y2:
+  //    -1 -1
+  //   +-----+
+  //   | 6  9|
+  //   | 7 10|
+  //   | 8 11|
+  //   +-----+
+  const auto errorY2{CFI_section(&sectionY2.raw(), &y2->raw(), lowersY2,
+      /*uppers=*/nullptr, /*strides=*/nullptr)};
+  ASSERT_EQ(errorY2, 0) << "CFI_section failed for Y2: " << errorY2;
+
+  RTNAME(Matmul)(result, sectionX2, *y, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 2);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 2);
+  EXPECT_EQ(result.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(1).Extent(), 2);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 4}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(0), 46);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(1), 67);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(2), 64);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(3), 94);
+  result.Destroy();
+
+  RTNAME(Matmul)(result, *x, sectionY2, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 2);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 2);
+  EXPECT_EQ(result.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(1).Extent(), 2);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 4}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(0), 46);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(1), 67);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(2), 64);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(3), 94);
+  result.Destroy();
+
+  RTNAME(Matmul)(result, sectionX2, sectionY2, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 2);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 2);
+  EXPECT_EQ(result.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(1).Extent(), 2);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 4}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(0), 46);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(1), 67);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(2), 64);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(3), 94);
+  result.Destroy();
+
+  RTNAME(Matmul)(result, *v, sectionX2, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 1);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 3);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 8}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(0), -2);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(1), -8);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(2), -14);
+  result.Destroy();
+
+  RTNAME(Matmul)(result, sectionY2, *v, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 1);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 3);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 8}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(0), -24);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(1), -27);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(2), -30);
+  result.Destroy();
+
   // X F F T  Y F T
   //   F T T    F T
   //            F F
diff --git a/flang/unittests/Runtime/MatmulTranspose.cpp b/flang/unittests/Runtime/MatmulTranspose.cpp
--- a/flang/unittests/Runtime/MatmulTranspose.cpp
+++ b/flang/unittests/Runtime/MatmulTranspose.cpp
@@ -32,6 +32,17 @@
       std::vector<std::int16_t>{0, 0, 0, 1, 1, 0, 1, 1})};
   auto v{MakeArray<TypeCategory::Integer, 8>(
       std::vector<int>{2}, std::vector<std::int64_t>{-1, -2})};
+  // X2  0  1     Y2 -1 -1     Z2  6  7  8
+  //     2  3         6  9         9 10 11
+  //     4  5         7 10        -1 -1 -1
+  //    -1 -1         8 11
+  auto x2{MakeArray<TypeCategory::Integer, 4>(std::vector<int>{4, 2},
+      std::vector<std::int32_t>{0, 2, 4, -1, 1, 3, 5, -1})};
+  auto y2{MakeArray<TypeCategory::Integer, 2>(std::vector<int>{4, 2},
+      std::vector<std::int16_t>{-1, 6, 7, 8, -1, 9, 10, 11})};
+  auto z2{MakeArray<TypeCategory::Integer, 2>(std::vector<int>{3, 3},
+      std::vector<std::int16_t>{6, 9, -1, 7, 10, -1, 8, 11, -1})};
+
   StaticDescriptor<2, true> statDesc;
   Descriptor &result{statDesc.descriptor()};
 
@@ -89,6 +100,104 @@
   EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int16_t>(11), 19);
   result.Destroy();
 
+  // Test non-contiguous sections.
+  static constexpr int sectionRank{2};
+  StaticDescriptor<sectionRank> sectionStaticDescriptorX2;
+  Descriptor &sectionX2{sectionStaticDescriptorX2.descriptor()};
+  sectionX2.Establish(x2->type(), x2->ElementBytes(),
+      /*p=*/nullptr, /*rank=*/sectionRank);
+  static const SubscriptValue lowersX2[]{1, 1}, uppersX2[]{3, 2};
+  // Section of X2:
+  //   +-----+
+  //   | 0  1|
+  //   | 2  3|
+  //   | 4  5|
+  //   +-----+
+  //    -1 -1
+  const auto errorX2{CFI_section(
+      &sectionX2.raw(), &x2->raw(), lowersX2, uppersX2, /*strides=*/nullptr)};
+  ASSERT_EQ(errorX2, 0) << "CFI_section failed for X2: " << errorX2;
+
+  StaticDescriptor<sectionRank> sectionStaticDescriptorY2;
+  Descriptor &sectionY2{sectionStaticDescriptorY2.descriptor()};
+  sectionY2.Establish(y2->type(), y2->ElementBytes(),
+      /*p=*/nullptr, /*rank=*/sectionRank);
+  static const SubscriptValue lowersY2[]{2, 1};
+  // Section of Y2:
+  //    -1 -1
+  //   +-----+
+  //   | 6  0|
+  //   | 7 10|
+  //   | 8 11|
+  //   +-----+
+  const auto errorY2{CFI_section(&sectionY2.raw(), &y2->raw(), lowersY2,
+      /*uppers=*/nullptr, /*strides=*/nullptr)};
+  ASSERT_EQ(errorY2, 0) << "CFI_section failed for Y2: " << errorY2;
+
+  StaticDescriptor<sectionRank> sectionStaticDescriptorZ2;
+  Descriptor &sectionZ2{sectionStaticDescriptorZ2.descriptor()};
+  sectionZ2.Establish(z2->type(), z2->ElementBytes(),
+      /*p=*/nullptr, /*rank=*/sectionRank);
+  static const SubscriptValue lowersZ2[]{1, 1}, uppersZ2[]{2, 3};
+  // Section of Z2:
+  //   +--------+
+  //   | 6  7  8|
+  //   | 9 10 11|
+  //   +--------+
+  //    -1 -1 -1
+  const auto errorZ2{CFI_section(
+      &sectionZ2.raw(), &z2->raw(), lowersZ2, uppersZ2, /*strides=*/nullptr)};
+  ASSERT_EQ(errorZ2, 0) << "CFI_section failed for Z2: " << errorZ2;
+
+  RTNAME(MatmulTranspose)(result, sectionX2, *y, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 2);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 2);
+  EXPECT_EQ(result.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(1).Extent(), 2);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 4}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(0), 46);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(1), 67);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(2), 64);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(3), 94);
+  result.Destroy();
+
+  RTNAME(MatmulTranspose)(result, *x, sectionY2, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 2);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 2);
+  EXPECT_EQ(result.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(1).Extent(), 2);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 4}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(0), 46);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(1), 67);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(2), 64);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(3), 94);
+  result.Destroy();
+
+  RTNAME(MatmulTranspose)(result, sectionX2, sectionY2, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 2);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 2);
+  EXPECT_EQ(result.GetDimension(1).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(1).Extent(), 2);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 4}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(0), 46);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(1), 67);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(2), 64);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int32_t>(3), 94);
+  result.Destroy();
+
+  RTNAME(MatmulTranspose)(result, sectionZ2, *v, __FILE__, __LINE__);
+  ASSERT_EQ(result.rank(), 1);
+  EXPECT_EQ(result.GetDimension(0).LowerBound(), 1);
+  EXPECT_EQ(result.GetDimension(0).Extent(), 3);
+  ASSERT_EQ(result.type(), (TypeCode{TypeCategory::Integer, 8}));
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(0), -24);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(1), -27);
+  EXPECT_EQ(*result.ZeroBasedIndexedElement<std::int64_t>(2), -30);
+  result.Destroy();
+
   // X F F    Y F T    V T F T
   //   T F      F T
   //   T T      F F