diff --git a/mlir/lib/IR/BuiltinTypes.cpp b/mlir/lib/IR/BuiltinTypes.cpp
--- a/mlir/lib/IR/BuiltinTypes.cpp
+++ b/mlir/lib/IR/BuiltinTypes.cpp
@@ -673,26 +673,23 @@
                                         SmallVectorImpl<AffineExpr> &strides,
                                         AffineExpr &offset) {
   auto affineMaps = t.getAffineMaps();
-  // For now strides are only computed on a single affine map with a single
-  // result (i.e. the closed subset of linearization maps that are compatible
-  // with striding semantics).
-  // TODO: support more forms on a per-need basis.
-  if (affineMaps.size() > 1)
-    return failure();
-  if (affineMaps.size() == 1 && affineMaps[0].getNumResults() != 1)
-    return failure();
 
-  auto zero = getAffineConstantExpr(0, t.getContext());
-  auto one = getAffineConstantExpr(1, t.getContext());
-  offset = zero;
-  strides.assign(t.getRank(), zero);
+  if (!affineMaps.empty() && affineMaps.back().getNumResults() != 1)
+    return failure();
 
   AffineMap m;
   if (!affineMaps.empty()) {
-    m = affineMaps.front();
+    m = affineMaps.back();
+    for (size_t i = affineMaps.size() - 1; i > 0; --i)
+      m = m.compose(affineMaps[i - 1]);
     assert(!m.isIdentity() && "unexpected identity map");
   }
 
+  auto zero = getAffineConstantExpr(0, t.getContext());
+  auto one = getAffineConstantExpr(1, t.getContext());
+  offset = zero;
+  strides.assign(t.getRank(), zero);
+
   // Canonical case for empty map.
   if (!m) {
     // 0-D corner case, offset is already 0.
diff --git a/mlir/test/Dialect/Affine/memref-stride-calculation.mlir b/mlir/test/Dialect/Affine/memref-stride-calculation.mlir
--- a/mlir/test/Dialect/Affine/memref-stride-calculation.mlir
+++ b/mlir/test/Dialect/Affine/memref-stride-calculation.mlir
@@ -60,7 +60,8 @@
 // CHECK: MemRefType offset: 123 strides:
 
   %100 = memref.alloc(%0, %0)[%0, %0] : memref<?x?x16xf32, affine_map<(i, j, k)[M, N]->(i + j, j, k)>, affine_map<(i, j, k)[M, N]->(M * i + N * j + k + 1)>>
-// CHECK: MemRefType memref<?x?x16xf32, affine_map<(d0, d1, d2)[s0, s1] -> (d0 + d1, d1, d2)>, affine_map<(d0, d1, d2)[s0, s1] -> (d0 * s0 + d1 * s1 + d2 + 1)>> cannot be converted to strided form
+  // CHECK: MemRefType offset: 1 strides: ?, ?, 1
+
   %101 = memref.alloc() : memref<3x4x5xf32, affine_map<(i, j, k)->(i floordiv 4 + j + k)>>
 // CHECK: MemRefType memref<3x4x5xf32, affine_map<(d0, d1, d2) -> (d0 floordiv 4 + d1 + d2)>> cannot be converted to strided form
   %102 = memref.alloc() : memref<3x4x5xf32, affine_map<(i, j, k)->(i ceildiv 4 + j + k)>>
diff --git a/mlir/unittests/IR/CMakeLists.txt b/mlir/unittests/IR/CMakeLists.txt
--- a/mlir/unittests/IR/CMakeLists.txt
+++ b/mlir/unittests/IR/CMakeLists.txt
@@ -1,6 +1,7 @@
 add_mlir_unittest(MLIRIRTests
   AttributeTest.cpp
   DialectTest.cpp
+  MemRefTypeTest.cpp
   OperationSupportTest.cpp
   ShapedTypeTest.cpp
 )
diff --git a/mlir/unittests/IR/MemRefTypeTest.cpp b/mlir/unittests/IR/MemRefTypeTest.cpp
new file mode 100644
--- /dev/null
+++ b/mlir/unittests/IR/MemRefTypeTest.cpp
@@ -0,0 +1,50 @@
+//===- MemRefTypeTest.cpp - MemRefType unit tests -------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/IR/AffineMap.h"
+#include "mlir/IR/BuiltinTypes.h"
+#include "gtest/gtest.h"
+
+using namespace mlir;
+using namespace mlir::detail;
+
+namespace {
+
+TEST(MemRefTypeTest, GetStridesAndOffset) {
+  MLIRContext context;
+
+  SmallVector<int64_t> shape({2, 3, 4});
+  Type f32 = FloatType::getF32(&context);
+
+  AffineMap map1 = makeStridedLinearLayoutMap({12, 4, 1}, 5, &context);
+  MemRefType type1 = MemRefType::get(shape, f32, {map1});
+  SmallVector<int64_t> strides1;
+  int64_t offset1 = -1;
+  LogicalResult res1 = getStridesAndOffset(type1, strides1, offset1);
+  ASSERT_TRUE(res1.succeeded());
+  ASSERT_EQ(3, strides1.size());
+  EXPECT_EQ(12, strides1[0]);
+  EXPECT_EQ(4, strides1[1]);
+  EXPECT_EQ(1, strides1[2]);
+  ASSERT_EQ(5, offset1);
+
+  AffineMap map2 = AffineMap::getPermutationMap({1, 2, 0}, &context);
+  AffineMap map3 = makeStridedLinearLayoutMap({8, 2, 1}, 0, &context);
+  MemRefType type2 = MemRefType::get(shape, f32, {map2, map3});
+  SmallVector<int64_t> strides2;
+  int64_t offset2 = -1;
+  LogicalResult res2 = getStridesAndOffset(type2, strides2, offset2);
+  ASSERT_TRUE(res2.succeeded());
+  ASSERT_EQ(3, strides2.size());
+  EXPECT_EQ(1, strides2[0]);
+  EXPECT_EQ(8, strides2[1]);
+  EXPECT_EQ(2, strides2[2]);
+  ASSERT_EQ(0, offset2);
+}
+
+} // end namespace