diff --git a/docs/api/utilities.rst b/docs/api/utilities.rst
index 816f82ee..9b909431 100644
--- a/docs/api/utilities.rst
+++ b/docs/api/utilities.rst
@@ -100,6 +100,7 @@ Tree
     tree_l1_norm
     tree_l2_norm
     tree_map_params
+    tree_max
     tree_mul
     tree_ones_like
     tree_random_like
@@ -156,6 +157,10 @@ Tree map parameters
 ~~~~~~~~~~~~~~~~~~~
 .. autofunction:: tree_map_params
 
+Tree max
+~~~~~~~~
+.. autofunction:: tree_max
+
 Tree multiply
 ~~~~~~~~~~~~~
 .. autofunction:: tree_mul
diff --git a/optax/tree_utils/__init__.py b/optax/tree_utils/__init__.py
index d984a100..9675ad02 100644
--- a/optax/tree_utils/__init__.py
+++ b/optax/tree_utils/__init__.py
@@ -32,6 +32,7 @@
 from optax.tree_utils._tree_math import tree_full_like
 from optax.tree_utils._tree_math import tree_l1_norm
 from optax.tree_utils._tree_math import tree_l2_norm
+from optax.tree_utils._tree_math import tree_max
 from optax.tree_utils._tree_math import tree_mul
 from optax.tree_utils._tree_math import tree_ones_like
 from optax.tree_utils._tree_math import tree_scalar_mul
diff --git a/optax/tree_utils/_tree_math.py b/optax/tree_utils/_tree_math.py
index 13673549..3d52c23c 100644
--- a/optax/tree_utils/_tree_math.py
+++ b/optax/tree_utils/_tree_math.py
@@ -168,6 +168,20 @@ def tree_sum(tree: Any) -> chex.Numeric:
   return jax.tree.reduce(operator.add, sums, initializer=0)
 
 
+def tree_max(tree: Any) -> chex.Numeric:
+  """Compute the max of all the elements in a pytree.
+
+  Args:
+    tree: pytree.
+
+  Returns:
+    a scalar value.
+  """
+  maxes = jax.tree.map(jnp.max, tree)
+  # initializer=-jnp.inf should work but pytype wants a jax.Array.
+  return jax.tree.reduce(jnp.maximum, maxes, initializer=jnp.array(-jnp.inf))
+
+
 def _square(leaf):
   return jnp.square(leaf.real) + jnp.square(leaf.imag)
 
diff --git a/optax/tree_utils/_tree_math_test.py b/optax/tree_utils/_tree_math_test.py
index f0f326ce..054f239d 100644
--- a/optax/tree_utils/_tree_math_test.py
+++ b/optax/tree_utils/_tree_math_test.py
@@ -133,6 +133,16 @@ def test_tree_sum(self):
     got = tu.tree_sum(self.tree_a)
     np.testing.assert_allclose(expected, got)
 
+  @parameterized.parameters(
+      'array_a', 'tree_a', 'tree_a_dict', 'tree_b', 'tree_b_dict'
+  )
+  def test_tree_max(self, key):
+    tree = self.data[key]
+    values, _ = flatten_util.ravel_pytree(tree)
+    expected = jnp.max(values)
+    got = tu.tree_max(tree)
+    np.testing.assert_allclose(expected, got)
+
   def test_tree_l2_norm(self):
     expected = jnp.sqrt(jnp.vdot(self.array_a, self.array_a).real)
     got = tu.tree_l2_norm(self.array_a)