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
@@ -146,6 +146,8 @@
   let results = (outs I1:$result);
 
   let assemblyFormat = "$lhs `,` $rhs `:` type($lhs) attr-dict";
+
+  let hasFolder = 1;
 }
 
 def Shape_FromExtentsOp : Shape_Op<"from_extents", [NoSideEffect]> {
diff --git a/mlir/include/mlir/IR/Builders.h b/mlir/include/mlir/IR/Builders.h
--- a/mlir/include/mlir/IR/Builders.h
+++ b/mlir/include/mlir/IR/Builders.h
@@ -109,6 +109,7 @@
   FloatAttr getF32FloatAttr(float value);
   FloatAttr getF64FloatAttr(double value);
 
+  IntegerAttr getI1IntegerAttr(int8_t value);
   IntegerAttr getI8IntegerAttr(int8_t value);
   IntegerAttr getI16IntegerAttr(int16_t value);
   IntegerAttr getI32IntegerAttr(int32_t value);
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
@@ -380,6 +380,26 @@
 
 OpFoldResult ConstWitnessOp::fold(ArrayRef<Attribute>) { return passingAttr(); }
 
+//===----------------------------------------------------------------------===//
+// EqOp
+//===----------------------------------------------------------------------===//
+
+OpFoldResult EqOp::fold(ArrayRef<Attribute> operands) {
+
+  // Fold size equality.
+  if (auto lhs = operands[0].dyn_cast_or_null<IntegerAttr>()) {
+    if (auto rhs = operands[1].dyn_cast_or_null<IntegerAttr>()) {
+      bool eq = lhs.getValue().eq(rhs.getValue());
+      Builder builder(getContext());
+      return builder.getI1IntegerAttr(eq);
+    }
+  }
+
+  // TODO: Fold shape equality.
+
+  return {};
+}
+
 //===----------------------------------------------------------------------===//
 // IndexToSizeOp
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/IR/Builders.cpp b/mlir/lib/IR/Builders.cpp
--- a/mlir/lib/IR/Builders.cpp
+++ b/mlir/lib/IR/Builders.cpp
@@ -165,6 +165,10 @@
   return IntegerAttr::get(getIntegerType(8), APInt(8, value));
 }
 
+IntegerAttr Builder::getI1IntegerAttr(int8_t value) {
+  return IntegerAttr::get(getI1Type(), value);
+}
+
 IntegerAttr Builder::getIntegerAttr(Type type, int64_t value) {
   if (type.isIndex())
     return IntegerAttr::get(type, APInt(64, value));
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
@@ -442,3 +442,44 @@
   "consume.witness"(%0) : (!shape.witness) -> ()
   return
 }
+
+// -----
+
+// Fold `eq` for equal and constant sizes.
+// CHECK-LABEL: @eq_size_fold_1
+func @eq_size_fold_1() -> i1 {
+  // CHECK: %[[RESULT:.*]] = constant true
+  // CHECK: return %[[RESULT]] : i1
+  %a = shape.const_size 123
+  %b = shape.const_size 123
+  %result = shape.eq %a, %b : !shape.size
+  return %result : i1
+}
+
+// -----
+
+// Fold `eq` for different but constant sizes.
+// CHECK-LABEL: @eq_size_fold_0
+func @eq_size_fold_0() -> i1 {
+  // CHECK: %[[RESULT:.*]] = constant false
+  // CHECK: return %[[RESULT]] : i1
+  %a = shape.const_size 123
+  %b = shape.const_size 456
+  %result = shape.eq %a, %b : !shape.size
+  return %result : i1
+}
+
+// -----
+
+// Do not fold `eq` for non-constant sizes.
+// CHECK-LABEL: @eq_size_do_not_fold
+// CHECK-SAME: (%[[A:.*]]: !shape.size) -> i1
+func @eq_size_do_not_fold(%a : !shape.size) -> i1 {
+  // CHECK: %[[B:.*]] = shape.const_size 456
+  // CHECK: %[[RESULT:.*]] = shape.eq %[[A]], %[[B]] : !shape.size
+  // CHECK: return %[[RESULT]] : i1
+  %b = shape.const_size 456
+  %result = shape.eq %a, %b : !shape.size
+  return %result : i1
+}
+