diff --git a/mlir/lib/Conversion/ShapeToSCF/ShapeToSCF.cpp b/mlir/lib/Conversion/ShapeToSCF/ShapeToSCF.cpp
--- a/mlir/lib/Conversion/ShapeToSCF/ShapeToSCF.cpp
+++ b/mlir/lib/Conversion/ShapeToSCF/ShapeToSCF.cpp
@@ -19,6 +19,92 @@
 using namespace mlir::shape;
 using namespace mlir::scf;
 
+namespace {
+/// Converts `shape.shape_eq` to an `scf.for` loop. For now, the lowering is
+/// only defined on `tensor<?xindex>` operands. The test for equality first
+/// compares their size and, if equal, checks every extent for equality.
+///
+/// Example:
+///
+/// %result = shape.shape_eq %a, %b : tensor<?xindex>, tensor<?xindex>
+///
+/// becomes
+///
+/// %c0 = constant 0 : index
+/// %0 = dim %arg0, %c0 : tensor<?xindex>
+/// %1 = dim %arg1, %c0 : tensor<?xindex>
+/// %2 = cmpi "eq", %0, %1 : index
+/// %result = scf.if %2 -> (i1) {
+///   %c1 = constant 1 : index
+///   %true = constant true
+///   %4 = scf.for %arg2 = %c0 to %0 step %c1 iter_args(%arg3 = %true) -> (i1) {
+///     %5 = extract_element %arg0[%arg2] : tensor<?xindex>
+///     %6 = extract_element %arg1[%arg2] : tensor<?xindex>
+///     %7 = cmpi "eq", %5, %6 : index
+///     %8 = and %arg3, %7 : i1
+///     scf.yield %8 : i1
+///   }
+///   scf.yield %4 : i1
+/// } else {
+///   %false = constant false
+///   scf.yield %false : i1
+/// }
+///
+struct ShapeEqOpConverter : public OpConversionPattern<ShapeEqOp> {
+  using OpConversionPattern<ShapeEqOp>::OpConversionPattern;
+
+  LogicalResult
+  matchAndRewrite(ShapeEqOp op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override;
+};
+} // namespace
+
+LogicalResult
+ShapeEqOpConverter::matchAndRewrite(ShapeEqOp op, ArrayRef<Value> operands,
+                                    ConversionPatternRewriter &rewriter) const {
+  // For now, this lowering is only defined on `tensor<?xindex>` operands, not
+  // on shapes.
+  if (op.lhs().getType().isa<ShapeType>() ||
+      op.rhs().getType().isa<ShapeType>()) {
+    return failure();
+  }
+
+  ShapeEqOp::Adaptor transformed(operands);
+  auto loc = op.getLoc();
+  Type indexTy = rewriter.getIndexType();
+  Value zero = rewriter.create<ConstantIndexOp>(loc, 0);
+  Value lhsRank = rewriter.create<DimOp>(loc, indexTy, transformed.lhs(), zero);
+  Value rhsRank = rewriter.create<DimOp>(loc, indexTy, transformed.rhs(), zero);
+  Value eqRank =
+      rewriter.create<CmpIOp>(loc, CmpIPredicate::eq, lhsRank, rhsRank);
+  Type i1Ty = rewriter.getI1Type();
+  rewriter.replaceOpWithNewOp<IfOp>(
+      op, i1Ty, eqRank,
+      [&](OpBuilder &b, Location loc) {
+        Value one = b.create<ConstantIndexOp>(loc, 1);
+        Value init = b.create<ConstantOp>(loc, i1Ty, b.getBoolAttr(true));
+        auto loop = b.create<scf::ForOp>(
+            loc, zero, lhsRank, one, ValueRange{init},
+            [&](OpBuilder &b, Location nestedLoc, Value iv, ValueRange args) {
+              Value conj = args[0];
+              Value lhsExtent =
+                  b.create<ExtractElementOp>(loc, transformed.lhs(), iv);
+              Value rhsExtent =
+                  b.create<ExtractElementOp>(loc, transformed.rhs(), iv);
+              Value eqExtent = b.create<CmpIOp>(loc, CmpIPredicate::eq,
+                                                lhsExtent, rhsExtent);
+              Value conjNext = b.create<AndOp>(loc, conj, eqExtent);
+              b.create<scf::YieldOp>(loc, ValueRange({conjNext}));
+            });
+        b.create<scf::YieldOp>(loc, loop.getResults());
+      },
+      [&](OpBuilder &b, Location loc) {
+        Value result = b.create<ConstantOp>(loc, i1Ty, b.getBoolAttr(false));
+        b.create<scf::YieldOp>(loc, result);
+      });
+  return success();
+}
+
 namespace {
 /// Converts `shape.reduce` to `scf.for`.
 struct ReduceOpConverter : public OpConversionPattern<shape::ReduceOp> {
@@ -148,7 +234,12 @@
 
 void mlir::populateShapeToSCFConversionPatterns(
     OwningRewritePatternList &patterns, MLIRContext *ctx) {
-  patterns.insert<ReduceOpConverter, ShapeOfOpConverter>(ctx);
+  // clang-format off
+  patterns.insert<
+      ShapeEqOpConverter,
+      ReduceOpConverter,
+      ShapeOfOpConverter>(ctx);
+  // clang-format on
 }
 
 std::unique_ptr<FunctionPass> mlir::createConvertShapeToSCFPass() {
diff --git a/mlir/test/Conversion/ShapeToSCF/shape-to-scf.mlir b/mlir/test/Conversion/ShapeToSCF/shape-to-scf.mlir
--- a/mlir/test/Conversion/ShapeToSCF/shape-to-scf.mlir
+++ b/mlir/test/Conversion/ShapeToSCF/shape-to-scf.mlir
@@ -43,3 +43,31 @@
   return
 }
 
+// -----
+
+// CHECK-LABEL:  @shape_eq
+// CHECK-SAME:   (%[[A:.*]]: tensor<?xindex>, %[[B:.*]]: tensor<?xindex>) -> i1
+func @shape_eq(%a : tensor<?xindex>, %b : tensor<?xindex>) -> i1 {
+  // CHECK: %[[C0:.*]] = constant 0 : index
+  // CHECK: %[[RANK_A:.*]] = dim %[[A]], %[[C0]] : tensor<?xindex>
+  // CHECK: %[[RANK_B:.*]] = dim %[[B]], %[[C0]] : tensor<?xindex>
+  // CHECK: %[[RANK_EQ:.*]] = cmpi "eq", %[[RANK_A]], %[[RANK_B]]
+  // CHECK: %[[SHAPE_EQ:.*]] = scf.if %[[RANK_EQ]] -> (i1) {
+  // CHECK:   %[[C1:.*]] = constant 1 : index
+  // CHECK:   %[[INIT:.*]] = constant true
+  // CHECK:   %[[SHAPE_EQ_INNER:.*]] = scf.for %[[I:.*]] = %[[C0]] to %[[RANK_A]] step %[[C1]] iter_args(%[[CONJ:.*]] = %[[INIT]]) -> (i1) {
+  // CHECK:     %[[EXTENT_A:.*]] = extract_element %[[A]][%[[I]]] : tensor<?xindex>
+  // CHECK:     %[[EXTENT_B:.*]] = extract_element %[[B]][%[[I]]] : tensor<?xindex>
+  // CHECK:     %[[EXTENT_EQ:.*]] = cmpi "eq", %[[EXTENT_A]], %[[EXTENT_B]]
+  // CHECK:     %[[CONJ_NEXT:.*]] = and %[[CONJ]], %[[EXTENT_EQ]]
+  // CHECK:     scf.yield %[[CONJ_NEXT]] : i1
+  // CHECK:   }
+  // CHECK:   scf.yield %[[SHAPE_EQ_INNER]] : i1
+  // CHECK: } else {
+  // CHECK:   %[[SHAPE_EQ_INNER:.*]] = constant false
+  // CHECK:   scf.yield %[[SHAPE_EQ_INNER]] : i1
+  // CHECK: }
+  // CHECK: return %[[SHAPE_EQ]] : i1
+  %result = shape.shape_eq %a, %b : tensor<?xindex>, tensor<?xindex>
+  return %result : i1
+}