diff --git a/backends/native/test/samples/BUCK b/backends/native/test/samples/BUCK
index 4a1054d1e89..434045d2916 100644
--- a/backends/native/test/samples/BUCK
+++ b/backends/native/test/samples/BUCK
@@ -12,6 +12,7 @@ fbcode_target(
         "linear.py",
         "ops.py",
         "record.py",
+        "rms_norm.py",
         "schemes.py",
     ],
     deps = [
diff --git a/backends/native/test/samples/ops.py b/backends/native/test/samples/ops.py
index 78ed6717d39..78f3b7b8d00 100644
--- a/backends/native/test/samples/ops.py
+++ b/backends/native/test/samples/ops.py
@@ -9,7 +9,7 @@
 from collections.abc import Callable
 from dataclasses import dataclass
 
-from executorch.backends.native.test.samples import embedding, linear
+from executorch.backends.native.test.samples import embedding, linear, rms_norm
 from executorch.backends.native.test.samples.cases import Case
 from executorch.backends.native.test.samples.record import DTYPES
 
@@ -21,4 +21,8 @@ class Op:
 
 
 def ops() -> dict[str, Op]:
-    return {"embedding": Op(embedding.cases), "linear": Op(linear.cases)}
+    return {
+        "embedding": Op(embedding.cases),
+        "linear": Op(linear.cases),
+        "rms_norm": Op(rms_norm.cases),
+    }
diff --git a/backends/native/test/samples/rms_norm.py b/backends/native/test/samples/rms_norm.py
new file mode 100644
index 00000000000..8d5e57cd79f
--- /dev/null
+++ b/backends/native/test/samples/rms_norm.py
@@ -0,0 +1,71 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the BSD-style license found in the
+# LICENSE file in the root directory of this source tree.
+
+"""RMSNorm cases: LLM hidden and head norms, with and without a weight, rows
+whose magnitude stresses eps and the sum of squares, and dynamic shapes."""
+
+import torch
+from executorch.backends.native.test.samples.cases import Case, chain, draws, Inputs
+from torch.export import Dim
+
+
+def _norm(dim: int, eps: float = 1e-5, affine: bool = True) -> torch.nn.RMSNorm:
+    norm = torch.nn.RMSNorm(dim, eps=eps, elementwise_affine=affine)
+    if affine:
+        torch.nn.init.uniform_(norm.weight, 0.5, 1.5)
+    return norm
+
+
+def _scaled_rows(inputs: list[Inputs], scales: list[float]) -> list[Inputs]:
+    for (x,) in inputs:
+        x *= torch.tensor(scales)[:, None]
+    return inputs
+
+
+def cases() -> list[Case]:
+    torch.manual_seed(0)
+    # One channel far above the rest, as in LLM activations.
+    outlier = draws(2, (16, 2048))
+    for (x,) in outlier:
+        x[:, 3] *= 1000
+    tokens, batch = Dim("tokens", min=1, max=64), Dim("batch", min=1, max=4)
+    return [
+        # A hidden size that is not a power of two.
+        Case("decode", _norm(6656), draws(8, (1, 6656))),
+        Case("prefill", _norm(2048), draws(2, (64, 2048))),
+        Case("no_weight", _norm(6656, affine=False), draws(4, (4, 6656))),
+        # Query and key norms over the head dim of [batch, tokens, heads, 128].
+        Case("head_norm", _norm(128), draws(4, (1, 16, 8, 128))),
+        Case(
+            "head_norm_no_weight",
+            _norm(128, affine=False),
+            draws(4, (1, 16, 8, 128)),
+        ),
+        # Rows down to a mean square below eps, and a zero row.
+        Case(
+            "tiny_rows",
+            _norm(6656, eps=1e-8),
+            _scaled_rows(
+                draws(2, (8, 6656)), [1, 1e-2, 1e-3, 3e-4, 1e-4, 3e-5, 1e-5, 0]
+            ),
+        ),
+        # Squares that overflow float16.
+        Case(
+            "large_rows",
+            _norm(2048),
+            _scaled_rows(draws(2, (4, 2048)), [1, 1e2, 1e3, 1e4]),
+        ),
+        Case("outlier_channel", _norm(2048), outlier),
+        Case("leading_batch", _norm(512), draws(4, (2, 7, 512))),
+        Case("odd_dim", _norm(1001), draws(4, (4, 1001))),
+        chain("dynamic_tokens", _norm(1024), (tokens, 1024)),
+        chain("dynamic_batch_tokens", _norm(512), (batch, tokens, 512)),
+        chain(
+            "dynamic_head_norm_no_weight",
+            _norm(128, affine=False),
+            (1, tokens, 8, 128),
+        ),
+    ]
diff --git a/backends/native/test/samples/test_record.py b/backends/native/test/samples/test_record.py
index 7c42f344951..4ce29253cb1 100644
--- a/backends/native/test/samples/test_record.py
+++ b/backends/native/test/samples/test_record.py
@@ -19,6 +19,7 @@
     draws,
     suite_cases,
 )
+from executorch.backends.native.test.samples.ops import ops
 from executorch.backends.native.test.samples.record import DTYPES, record
 from executorch.backends.native.test.samples.schemes import (
     Gguf,
@@ -125,6 +126,13 @@ def test_record_adds_no_8da4w_golden_without_a_linear(self) -> None:
             record([case], schemes()["int4wo_g32"], path, dtypes=["f32"])
             self.assertEqual(set(read_samples(str(path))), {"golden", "precise"})
 
+    def test_rms_norm_fits_only_the_float_scheme(self) -> None:
+        cases = ops()["rms_norm"].cases()
+        for name, scheme in schemes().items():
+            self.assertEqual(
+                any(scheme.fits(case.model) for case in cases), name == "float", name
+            )
+
     def test_chain_visits_each_dims_bounds_starting_mid_range(self) -> None:
         a, b = Dim("a", min=1, max=8), Dim("b", min=2, max=4)
         case = chain("pair", torch.nn.Identity(), (a, 3), (b, a))