diff --git a/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td b/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
--- a/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
+++ b/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
@@ -149,6 +149,7 @@
   let results = (outs I1:$result);
 
   let assemblyFormat = "$lhs `,` $rhs attr-dict";
+  let hasFolder = 1;
 }
 
 def Shape_FromExtentsOp : Shape_Op<"from_extents", [NoSideEffect]> {
diff --git a/mlir/lib/Dialect/Shape/IR/Shape.cpp b/mlir/lib/Dialect/Shape/IR/Shape.cpp
--- a/mlir/lib/Dialect/Shape/IR/Shape.cpp
+++ b/mlir/lib/Dialect/Shape/IR/Shape.cpp
@@ -385,6 +385,20 @@
 
 OpFoldResult ConstWitnessOp::fold(ArrayRef<Attribute>) { return passingAttr(); }
 
+//===----------------------------------------------------------------------===//
+// ShapeEqOp
+//===----------------------------------------------------------------------===//
+
+OpFoldResult ShapeEqOp::fold(ArrayRef<Attribute> operands) {
+  auto lhs = operands[0].dyn_cast_or_null<DenseIntElementsAttr>();
+  if (lhs == nullptr)
+    return {};
+  auto rhs = operands[1].dyn_cast_or_null<DenseIntElementsAttr>();
+  if (rhs == nullptr)
+    return {};
+  return BoolAttr::get(lhs == rhs, getContext());
+}
+
 //===----------------------------------------------------------------------===//
 // IndexToSizeOp
 //===----------------------------------------------------------------------===//
diff --git a/mlir/test/Dialect/Shape/canonicalize.mlir b/mlir/test/Dialect/Shape/canonicalize.mlir
--- a/mlir/test/Dialect/Shape/canonicalize.mlir
+++ b/mlir/test/Dialect/Shape/canonicalize.mlir
@@ -515,3 +515,55 @@
   return %result : !shape.size
 }
 
+// -----
+
+// Fold `shape_eq` for equal and constant shapes.
+// CHECK-LABEL: @shape_eq_fold_1
+func @shape_eq_fold_1() -> i1 {
+  // CHECK: %[[RESULT:.*]] = constant true
+  // CHECK: return %[[RESULT]] : i1
+  %a = shape.const_shape [1, 2, 3]
+  %b = shape.const_shape [1, 2, 3]
+  %result = shape.shape_eq %a, %b
+  return %result : i1
+}
+
+// -----
+
+// Fold `shape_eq` for different but constant shapes of same length.
+// CHECK-LABEL: @shape_eq_fold_0
+func @shape_eq_fold_0() -> i1 {
+  // CHECK: %[[RESULT:.*]] = constant false
+  // CHECK: return %[[RESULT]] : i1
+  %a = shape.const_shape [1, 2, 3]
+  %b = shape.const_shape [4, 5, 6]
+  %result = shape.shape_eq %a, %b
+  return %result : i1
+}
+
+// -----
+
+// Fold `shape_eq` for different but constant shapes of different length.
+// CHECK-LABEL: @shape_eq_fold_0
+func @shape_eq_fold_0() -> i1 {
+  // CHECK: %[[RESULT:.*]] = constant false
+  // CHECK: return %[[RESULT]] : i1
+  %a = shape.const_shape [1, 2, 3, 4, 5, 6]
+  %b = shape.const_shape [1, 2, 3]
+  %result = shape.shape_eq %a, %b
+  return %result : i1
+}
+
+// -----
+
+// Do not fold `shape_eq` for non-constant shapes.
+// CHECK-LABEL: @shape_eq_do_not_fold
+// CHECK-SAME: (%[[A:.*]]: !shape.shape) -> i1
+func @shape_eq_do_not_fold(%a : !shape.shape) -> i1 {
+  // CHECK: %[[B:.*]] = shape.const_shape [4, 5, 6]
+  // CHECK: %[[RESULT:.*]] = shape.shape_eq %[[A]], %[[B]]
+  // CHECK: return %[[RESULT]] : i1
+  %b = shape.const_shape [4, 5, 6]
+  %result = shape.shape_eq %a, %b
+  return %result : i1
+}