diff --git a/mlir/include/mlir/Dialect/Math/IR/MathOps.td b/mlir/include/mlir/Dialect/Math/IR/MathOps.td
--- a/mlir/include/mlir/Dialect/Math/IR/MathOps.td
+++ b/mlir/include/mlir/Dialect/Math/IR/MathOps.td
@@ -677,6 +677,7 @@
     %a = math.tanh %b : f64
     ```
   }];
+  let hasFolder = 1;
 }
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/Dialect/Math/IR/MathOps.cpp b/mlir/lib/Dialect/Math/IR/MathOps.cpp
--- a/mlir/lib/Dialect/Math/IR/MathOps.cpp
+++ b/mlir/lib/Dialect/Math/IR/MathOps.cpp
@@ -282,6 +282,24 @@
       });
 }
 
+//===----------------------------------------------------------------------===//
+// TanhOp folder
+//===----------------------------------------------------------------------===//
+
+OpFoldResult math::TanhOp::fold(ArrayRef<Attribute> operands) {
+  return constFoldUnaryOpConditional<FloatAttr>(
+      operands, [](const APFloat &a) -> Optional<APFloat> {
+        switch (a.getSizeInBits(a.getSemantics())) {
+        case 64:
+          return APFloat(tanh(a.convertToDouble()));
+        case 32:
+          return APFloat(tanhf(a.convertToFloat()));
+        default:
+          return {};
+        }
+      });
+}
+
 /// Materialize an integer or floating point constant.
 Operation *math::MathDialect::materializeConstant(OpBuilder &builder,
                                                   Attribute value, Type type,
diff --git a/mlir/test/Dialect/Math/canonicalize.mlir b/mlir/test/Dialect/Math/canonicalize.mlir
--- a/mlir/test/Dialect/Math/canonicalize.mlir
+++ b/mlir/test/Dialect/Math/canonicalize.mlir
@@ -302,3 +302,21 @@
   return %0 : vector<4xf32>
 }
 
+// CHECK-LABEL: @tanh_fold
+// CHECK-NEXT: %[[cst:.+]] = arith.constant 0.761594176 : f32
+// CHECK-NEXT:   return %[[cst]]
+func.func @tanh_fold() -> f32 {
+  %c = arith.constant 1.0 : f32
+  %r = math.tanh %c : f32
+  return %r : f32
+}
+
+// CHECK-LABEL: @tanh_fold_vec
+// CHECK-NEXT: %[[cst:.+]] = arith.constant dense<[0.000000e+00, 0.761594176, 0.000000e+00, 0.761594176]> : vector<4xf32>
+// CHECK-NEXT:   return %[[cst]]
+func.func @tanh_fold_vec() -> (vector<4xf32>) {
+  %v1 = arith.constant dense<[0.0, 1.0, 0.0, 1.0]> : vector<4xf32>
+  %0 = math.tanh %v1 : vector<4xf32>
+  return %0 : vector<4xf32>
+}
+