diff --git a/mlir/lib/Conversion/ShapeToStandard/ShapeToStandard.cpp b/mlir/lib/Conversion/ShapeToStandard/ShapeToStandard.cpp
--- a/mlir/lib/Conversion/ShapeToStandard/ShapeToStandard.cpp
+++ b/mlir/lib/Conversion/ShapeToStandard/ShapeToStandard.cpp
@@ -90,6 +90,28 @@
   }
 };
 
+class EqOpConverter : public OpConversionPattern<EqOp> {
+public:
+  using OpConversionPattern<EqOp>::OpConversionPattern;
+
+  LogicalResult
+  matchAndRewrite(EqOp op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    auto operandTy = op.lhs().getType();
+
+    // Shape equality is lowered to `scf` and the pattern can be found in the
+    // corresponding pass.
+    if (!operandTy.isa<SizeType>())
+      return failure();
+
+    // Lower size equality.
+    EqOp::Adaptor transformed(operands);
+    rewriter.replaceOpWithNewOp<CmpIOp>(op, CmpIPredicate::eq,
+                                        transformed.lhs(), transformed.rhs());
+    return success();
+  }
+};
+
 /// Type conversions.
 class ShapeTypeConverter : public TypeConverter {
 public:
@@ -147,6 +169,7 @@
       BinaryOpConversion<AddOp, AddIOp>,
       BinaryOpConversion<MulOp, MulIOp>,
       ConstSizeOpConverter,
+      EqOpConverter,
       ShapeOfOpConversion>(ctx);
   // clang-format on
 }
diff --git a/mlir/test/Conversion/ShapeToStandard/shape-to-standard.mlir b/mlir/test/Conversion/ShapeToStandard/shape-to-standard.mlir
--- a/mlir/test/Conversion/ShapeToStandard/shape-to-standard.mlir
+++ b/mlir/test/Conversion/ShapeToStandard/shape-to-standard.mlir
@@ -115,3 +115,16 @@
   %shape = shape.shape_of %arg : tensor<1x5x?xf32>
   return
 }
+
+// -----
+
+// Lower `eq` for sizes.
+// CHECK-LABEL: @eq_size
+// CHECK-SAME: (%[[A:.*]]: index, %[[B:.*]]: index) -> i1
+func @eq_size(%a : !shape.size, %b : !shape.size) -> i1 {
+  // CHECK: %[[RESULT:.*]] = cmpi "eq", %[[A]], %[[B]]
+  // CHECK: return %[[RESULT]] : i1
+  %result = shape.eq %a, %b : !shape.size
+  return %result : i1
+}
+