diff --git a/tools/workspace/drake_models/BUILD.bazel b/tools/workspace/drake_models/BUILD.bazel
index 67914ea7e0a0..5618a72c03c0 100644
--- a/tools/workspace/drake_models/BUILD.bazel
+++ b/tools/workspace/drake_models/BUILD.bazel
@@ -1,3 +1,22 @@
+load("//doc:defs.bzl", "enumerate_filegroup")
+load("//tools/skylark:drake_py.bzl", "drake_py_unittest")
 load("//tools/lint:lint.bzl", "add_lint_tests")
 
+enumerate_filegroup(
+    name = "inventory.txt",
+    data = ["@drake_models"],
+)
+
+drake_py_unittest(
+    name = "parse_test",
+    data = [
+        ":inventory.txt",
+        "@drake_models",
+    ],
+    deps = [
+        "//bindings/pydrake",
+        "@bazel_tools//tools/python/runfiles",
+    ],
+)
+
 add_lint_tests()
diff --git a/tools/workspace/drake_models/test/parse_test.py b/tools/workspace/drake_models/test/parse_test.py
new file mode 100644
index 000000000000..c326dbdd9d61
--- /dev/null
+++ b/tools/workspace/drake_models/test/parse_test.py
@@ -0,0 +1,110 @@
+from pathlib import Path
+from typing import Iterator
+import unittest
+
+from bazel_tools.tools.python.runfiles import runfiles
+
+from pydrake.planning import RobotDiagramBuilder
+
+
+class TestDrakeModels(unittest.TestCase):
+
+    @staticmethod
+    def package_xml() -> Path:
+        """Returns the path to drake_models/package.xml in runfiles.
+        """
+        manifest = runfiles.Create()
+        result = Path(manifest.Rlocation("drake_models/package.xml"))
+        assert result.exists(), result
+        return result
+
+    @staticmethod
+    def inventory() -> Iterator[str]:
+        """Generates the list of all the runfiles of @drake_models. The result
+        is strings like "drake_models/veggies/pepper.png".
+        """
+        manifest = runfiles.Create()
+        inventory = Path(manifest.Rlocation(
+            "drake/tools/workspace/drake_models/inventory.txt"))
+        with open(inventory, encoding="utf-8") as f:
+            for line in f.readlines():
+                assert line.startswith("drake_models/")
+                yield line.strip()
+
+    @staticmethod
+    def get_all_models() -> Iterator[str]:
+        """Generates the Paths of all top-level model files in @drake_models.
+        The result is URLs like "package://drake_models/veggies/pepper.sdf".
+        """
+        for path in TestDrakeModels.inventory():
+            url = f"package://{path}"
+            if any([path.endswith(".dmd.yaml"),
+                    path.endswith(".sdf"),
+                    path.endswith(".urdf")]):
+                yield url
+            elif path.endswith(".xml"):
+                # We can't tell a MuJoCo file just by its suffix.
+                runfiles = TestDrakeModels.package_xml().parent.parent
+                if "<mujoco" in (runfiles / path).open().read():
+                    yield url
+        return
+
+    def test_all_models(self):
+        """Checks that all model files in @drake_models parse without any
+        errors nor warnings.
+        """
+        all_models = list(TestDrakeModels.get_all_models())
+
+        # Allow warnings on these models until they are repaired.
+        models_with_warnings = [
+            # TODO(#19992) for tracking these warnings.
+            "package://drake_models/atlas/atlas_convex_hull.urdf",
+            "package://drake_models/atlas/atlas_minimal_contact.urdf",
+            "package://drake_models/atlas/robotiq_simple.urdf",
+        ]
+        self.assertFalse(set(models_with_warnings) - set(all_models))
+
+        # Allow errors on these models until they are repaired.
+        models_with_errors = [
+            # TODO(#19992) for tracking these errors.
+            "package://drake_models/atlas/robotiq.urdf",
+            "package://drake_models/atlas/robotiq_tendons.urdf",
+        ]
+        self.assertFalse(set(models_with_errors) - set(all_models))
+        self.assertFalse(set(models_with_warnings) & set(models_with_errors))
+
+        # Run all tests.
+        for url in all_models:
+            with self.subTest(url=url):
+                expect_warnings = url in models_with_warnings
+                expect_errors = url in models_with_errors
+                self._check_model(
+                    url=url,
+                    expect_warnings=expect_warnings,
+                    expect_errors=expect_errors)
+
+    def _check_model(self, *,
+                     url: str,
+                     expect_warnings: bool,
+                     expect_errors: bool):
+        """Checks that when parsed, the given url contains warnings and/or
+        errors consistent with the expected conditions.
+        """
+        if expect_errors:
+            with self.assertRaises(Exception):
+                self._parse(url=url, strict=False)
+            return
+        if expect_warnings:
+            self._parse(url=url, strict=False)
+            with self.assertRaises(Exception):
+                self._parse(url=url, strict=True)
+            return
+        self._parse(url=url, strict=True)
+
+    def _parse(self, *, url: str, strict: bool):
+        builder = RobotDiagramBuilder()
+        parser = builder.parser()
+        parser.package_map().AddPackageXml(str(self.package_xml()))
+        if strict:
+            parser.SetStrictParsing()
+        parser.AddModels(url=url)