diff --git a/pytensor/link/jax/dispatch/tensor_basic.py b/pytensor/link/jax/dispatch/tensor_basic.py
index e70fd67b72..cc0385bf27 100644
--- a/pytensor/link/jax/dispatch/tensor_basic.py
+++ b/pytensor/link/jax/dispatch/tensor_basic.py
@@ -41,8 +41,20 @@ def allocempty(*shape):
 
 @jax_funcify.register(Alloc)
 def jax_funcify_Alloc(op, node, **kwargs):
+    static_shapes = []
+    for shape_input in node.inputs[1:]:
+        try:
+            static_shapes.append(int(get_scalar_constant_value(shape_input)))
+        except NotScalarConstantError:
+            concrete_shape = None
+            break
+    else:
+        concrete_shape = tuple(static_shapes)
+
     def alloc(x, *shape):
-        res = jnp.broadcast_to(x, shape)
+        res = jnp.broadcast_to(
+            x, concrete_shape if concrete_shape is not None else shape
+        )
         Alloc._check_runtime_broadcast(node, jnp.asarray(x), res.shape)
         return res