diff --git a/tests/scripts/generate_psa_tests.py b/tests/scripts/generate_psa_tests.py
index a164110..230bbd8 100755
--- a/tests/scripts/generate_psa_tests.py
+++ b/tests/scripts/generate_psa_tests.py
@@ -18,14 +18,34 @@
 # limitations under the License.
 
 import argparse
+import os
+import re
 import sys
-from typing import TypeVar
+from typing import Iterable, List, TypeVar
 
 import scripts_path # pylint: disable=unused-import
+from mbedtls_dev import crypto_knowledge
 from mbedtls_dev import macro_collector
+from mbedtls_dev import test_case
 
 T = TypeVar('T') #pylint: disable=invalid-name
 
+
+def test_case_for_key_type_not_supported(verb: str, key_type: str, bits: int,
+                                         dependencies: List[str],
+                                         *args: str) -> test_case.TestCase:
+    """Return one test case exercising a key creation method
+    for an unsupported key type or size.
+    """
+    tc = test_case.TestCase()
+    adverb = 'not' if dependencies else 'never'
+    tc.set_description('PSA {} {} {}-bit {} supported'
+                       .format(verb, key_type, bits, adverb))
+    tc.set_dependencies(dependencies)
+    tc.set_function(verb + '_not_supported')
+    tc.set_arguments([key_type] + list(args))
+    return tc
+
 class TestGenerator:
     """Gather information and generate test data."""
 
@@ -61,11 +81,62 @@
         self.remove_unwanted_macros(constructors)
         return constructors
 
+    def write_test_data_file(self, basename: str,
+                             test_cases: Iterable[test_case.TestCase]) -> None:
+        """Write the test cases to a .data file.
+
+        The output file is ``basename + '.data'`` in the test suite directory.
+        """
+        filename = os.path.join(self.test_suite_directory, basename + '.data')
+        test_case.write_data_file(filename, test_cases)
+
+    @staticmethod
+    def test_cases_for_key_type_not_supported(
+            kt: crypto_knowledge.KeyType
+    ) -> List[test_case.TestCase]:
+        """Return test cases exercising key creation when the given type is unsupported."""
+        if kt.name == 'PSA_KEY_TYPE_RAW_DATA':
+            # This key type is always supported.
+            return []
+        want_symbol = re.sub(r'\APSA_', r'PSA_WANT_', kt.name)
+        import_dependencies = ['!' + want_symbol]
+        if kt.name.endswith('_PUBLIC_KEY'):
+            generate_dependencies = []
+        else:
+            generate_dependencies = import_dependencies
+        test_cases = []
+        for bits in kt.sizes_to_test():
+            test_cases.append(test_case_for_key_type_not_supported(
+                'import', kt.name, bits, import_dependencies,
+                test_case.hex_string(kt.key_material(bits))
+            ))
+            test_cases.append(test_case_for_key_type_not_supported(
+                'generate', kt.name, bits, generate_dependencies,
+                str(bits)
+            ))
+            # To be added: derive
+        return test_cases
+
+    def generate_not_supported(self) -> None:
+        """Generate test cases that exercise the creation of keys of unsupported types."""
+        test_cases = []
+        for key_type in sorted(self.constructors.key_types):
+            kt = crypto_knowledge.KeyType(key_type)
+            test_cases += self.test_cases_for_key_type_not_supported(kt)
+        # To be added: parametrized key types (ECC, FFDH)
+        self.write_test_data_file(
+            'test_suite_psa_crypto_not_supported.generated',
+            test_cases)
+
+    def generate_all(self):
+        self.generate_not_supported()
+
 def main(args):
     """Command line entry point."""
     parser = argparse.ArgumentParser(description=__doc__)
     options = parser.parse_args(args)
     generator = TestGenerator(options)
+    generator.generate_all()
 
 if __name__ == '__main__':
     main(sys.argv[1:])