diff --git a/src/ome_zarr_models/base.py b/src/ome_zarr_models/base.py
index 91e8515..a9b4920 100644
--- a/src/ome_zarr_models/base.py
+++ b/src/ome_zarr_models/base.py
@@ -12,7 +12,8 @@ class Base(BaseModel):
         # This allows fields with aliases to be populated by either
         # their alias or class attribute name
         #
-        # We use this so we can handle (at least) the "bioformats2raw.version"
-        # key - attributes in Python can't contain a "."
+        # We use this so we can handle e.g., the "bioformats2raw.version"
+        # key - names in Python can't contain a "."
         populate_by_name=True,
+        frozen=True,
     )
diff --git a/tests/v04/test_multiscales.py b/tests/v04/test_multiscales.py
index e51632b..acf9266 100644
--- a/tests/v04/test_multiscales.py
+++ b/tests/v04/test_multiscales.py
@@ -55,6 +55,14 @@ def default_multiscale() -> Multiscale:
     return multi
 
 
+def test_immutable(default_multiscale: Multiscale) -> None:
+    """
+    Check that models are immutable.
+    """
+    with pytest.raises(ValidationError, match="Instance is frozen"):
+        default_multiscale.axes[0].name = "new_name"
+
+
 def test_multiscale_unique_axis_names() -> None:
     # TODO: is unique names actually part of the spec???
     axes = (