diff --git a/mlir/include/mlir/Dialect/Linalg/IR/LinalgNamedStructuredOps.yaml b/mlir/include/mlir/Dialect/Linalg/IR/LinalgNamedStructuredOps.yaml
--- a/mlir/include/mlir/Dialect/Linalg/IR/LinalgNamedStructuredOps.yaml
+++ b/mlir/include/mlir/Dialect/Linalg/IR/LinalgNamedStructuredOps.yaml
@@ -613,6 +613,55 @@
         - !ScalarExpression
           scalar_arg: rhs
 --- !LinalgOpConfig
+metadata: !LinalgOpMetadata
+  name: max
+  cpp_class_name: MaxOp
+  doc: |-
+    Takes the max (signed) between the input and a constant.
+
+    The shapes and element types must be identical. The appropriate casts,
+    broadcasts and reductions should be done previously to calling this op.
+
+    This means reduction/broadcast/element cast semantics is explicit. Further
+    passes can take that into account when lowering this code. For example,
+    a `linalg.broadcast` + `linalg.div` sequence can be lowered to a
+    `linalg.generic` with different affine maps for the two operands.
+structured_op: !LinalgStructuredOpConfig
+  args:
+  - !LinalgOperandDefConfig
+    name: lhs
+    kind: input_tensor
+    type_var: T
+    shape_map: affine_map<() -> ()>
+  - !LinalgOperandDefConfig
+    name: rhs
+    kind: input_tensor
+    type_var: T
+    shape_map: affine_map<() -> ()>
+  - !LinalgOperandDefConfig
+    name: out
+    kind: output_tensor
+    type_var: T
+    shape_map: affine_map<() -> ()>
+  indexing_maps: !LinalgIndexingMapsConfig
+    static_indexing_maps:
+    - affine_map<() -> ()>
+    - affine_map<() -> ()>
+    - affine_map<() -> ()>
+  iterator_types: []
+  assignments:
+  - !ScalarAssign
+    arg: out
+    value: !ScalarExpression
+      scalar_fn:
+        kind: binary
+        fn_name: max_signed
+        operands:
+        - !ScalarExpression
+          scalar_arg: lhs
+        - !ScalarExpression
+          scalar_arg: rhs
+--- !LinalgOpConfig
 metadata: !LinalgOpMetadata
   name: matmul
   cpp_class_name: MatmulOp
diff --git a/mlir/python/mlir/dialects/linalg/opdsl/ops/core_named_ops.py b/mlir/python/mlir/dialects/linalg/opdsl/ops/core_named_ops.py
--- a/mlir/python/mlir/dialects/linalg/opdsl/ops/core_named_ops.py
+++ b/mlir/python/mlir/dialects/linalg/opdsl/ops/core_named_ops.py
@@ -219,6 +219,25 @@
     O[None] = lhs[None] / rhs[None]
 
 
+@linalg_structured_op
+def max(
+    lhs=TensorDef(T1),
+    rhs=TensorDef(T1),
+    O=TensorDef(T1, output=True),
+):
+    """Takes the max (signed) between two inputs, elementwise.
+
+    The shapes and element types must be identical. The appropriate casts,
+    broadcasts and reductions should be done previously to calling this op.
+
+    This means reduction/broadcast/element cast semantics is explicit. Further
+    passes can take that into account when lowering this code. For example,
+    a `linalg.broadcast` + `linalg.div` sequence can be lowered to a
+    `linalg.generic` with different affine maps for the two operands.
+    """
+    O[None] = BinaryFn.max_signed(lhs[None], rhs[None])
+
+
 @linalg_structured_op
 def matmul(
     A=TensorDef(T1, S.M, S.K),
diff --git a/mlir/test/Dialect/Linalg/generalize-named-ops.mlir b/mlir/test/Dialect/Linalg/generalize-named-ops.mlir
--- a/mlir/test/Dialect/Linalg/generalize-named-ops.mlir
+++ b/mlir/test/Dialect/Linalg/generalize-named-ops.mlir
@@ -537,3 +537,28 @@
 // CHECK:         ^{{.+}}(%[[BBARG0:.+]]: f32, %[[BBARG1:.+]]: f32)
 // CHECK-NEXT:      %[[negf:.+]] = arith.negf %[[BBARG0]] : f32
 // CHECK-NEXT:      linalg.yield %[[negf]] : f32
+
+// -----
+
+func.func @generalize_max(%lhs: memref<7x14x21xf32>, %rhs: memref<7x14x21xf32>,
+                          %out: memref<7x14x21xf32>) {
+  linalg.max ins(%lhs, %rhs : memref<7x14x21xf32>, memref<7x14x21xf32>)
+             outs(%out : memref<7x14x21xf32>)
+  return
+}
+
+// CHECK: #[[MAP:.+]] = affine_map<(d0, d1, d2) -> (d0, d1, d2)>
+
+// CHECK: func @generalize_max
+// CHECK-SAME: (%[[LHS:.+]]: memref<7x14x21xf32>, %[[RHS:.+]]: memref<7x14x21xf32>,
+// CHECK-SAME:  %[[OUT:.+]]: memref<7x14x21xf32>)
+
+// CHECK: linalg.generic
+// CHECK-SAME: indexing_maps = [#[[MAP]], #[[MAP]], #[[MAP]]]
+// CHECK-SAME: iterator_types = ["parallel", "parallel", "parallel"]}
+// CHECK-SAME:  ins(%[[LHS]], %[[RHS]] : memref<7x14x21xf32>, memref<7x14x21xf32>)
+// CHECK-SAME: outs(%[[OUT]] : memref<7x14x21xf32>)
+
+// CHECK:         ^{{.+}}(%[[BBARG0:.+]]: f32, %[[BBARG1:.+]]: f32, %[[BBARG2:.+]]: f32)
+// CHECK-NEXT:      %[[max:.+]] = arith.maxf %[[BBARG0]], %[[BBARG1]] : f32
+// CHECK-NEXT:      linalg.yield %[[max]] : f32
diff --git a/mlir/test/Dialect/Linalg/named-ops-fail.mlir b/mlir/test/Dialect/Linalg/named-ops-fail.mlir
--- a/mlir/test/Dialect/Linalg/named-ops-fail.mlir
+++ b/mlir/test/Dialect/Linalg/named-ops-fail.mlir
@@ -173,3 +173,19 @@
   linalg.negf ins(%arg : memref<8x16xf32>) outs(%out: memref<4x8x16xf32>)
   return
 }
+
+// -----
+
+func.func @max_type_cast(%arg0: memref<4x8x16xf32>, %arg1: memref<4x8x16xf16>, %arg2: memref<4x8x16xf32>) {
+  // CHECK: op requires the same type for all operands and results
+  linalg.max ins(%arg0, %arg1 : memref<4x8x16xf32>, memref<4x8x16xf16>) outs(%arg2: memref<4x8x16xf32>)
+  return
+}
+
+// -----
+
+func.func @max_broadcast(%arg0: memref<8x16xf32>, %arg1: memref<4x8x16xf32>, %arg2: memref<4x8x16xf32>) {
+  // CHECK: op expected operand rank (2) to match the result rank of indexing_map #0 (3)
+  linalg.max ins(%arg0, %arg1 : memref<8x16xf32>, memref<4x8x16xf32>) outs(%arg2: memref<4x8x16xf32>)
+  return
+}
diff --git a/mlir/test/Dialect/Linalg/named-ops.mlir b/mlir/test/Dialect/Linalg/named-ops.mlir
--- a/mlir/test/Dialect/Linalg/named-ops.mlir
+++ b/mlir/test/Dialect/Linalg/named-ops.mlir
@@ -1540,3 +1540,37 @@
   %1 = linalg.negf ins(%arg0 : tensor<4x8x16xf32>) outs(%0: tensor<4x8x16xf32>) -> tensor<4x8x16xf32>
   return %1 : tensor<4x8x16xf32>
 }
+
+// -----
+
+// CHECK-LABEL: func @max_dynamic
+func.func @max_dynamic(%arg0: memref<?x?x?xf32>, %arg1: memref<?x?x?xf32>, %arg2: memref<?x?x?xf32>) {
+  // CHECK: linalg.max
+  // CHECK-SAME: ins(%{{.+}}, %{{.+}} : memref<?x?x?xf32>, memref<?x?x?xf32>)
+  // CHECK-SAME: outs(%{{.+}} : memref<?x?x?xf32>)
+  linalg.max ins(%arg0, %arg1 : memref<?x?x?xf32>, memref<?x?x?xf32>) outs(%arg2: memref<?x?x?xf32>)
+  return
+}
+
+// -----
+
+// CHECK-LABEL: func @max_static
+func.func @max_static(%arg0: memref<4x8x16xf32>, %arg1: memref<4x8x16xf32>, %arg2: memref<4x8x16xf32>) {
+  // CHECK: linalg.max
+  // CHECK-SAME: ins(%{{.+}}, %{{.+}} : memref<4x8x16xf32>, memref<4x8x16xf32>)
+  // CHECK-SAME: outs(%{{.+}} : memref<4x8x16xf32>)
+  linalg.max ins(%arg0, %arg1 : memref<4x8x16xf32>, memref<4x8x16xf32>) outs(%arg2: memref<4x8x16xf32>)
+  return
+}
+
+// -----
+
+// CHECK-LABEL: func @max_tensor
+func.func @max_tensor(%arg0: tensor<4x8x16xf32>, %arg1: tensor<4x8x16xf32>) -> tensor<4x8x16xf32> {
+  %0 = tensor.empty() : tensor<4x8x16xf32>
+  // CHECK: linalg.max
+  // CHECK-SAME: ins(%{{.+}}, %{{.+}} : tensor<4x8x16xf32>, tensor<4x8x16xf32>)
+  // CHECK-SAME: outs(%{{.+}} : tensor<4x8x16xf32>)
+  %1 = linalg.max ins(%arg0, %arg1 : tensor<4x8x16xf32>, tensor<4x8x16xf32>) outs(%0: tensor<4x8x16xf32>) -> tensor<4x8x16xf32>
+  return %1 : tensor<4x8x16xf32>
+}