diff --git a/test/ao/sparsity/test_composability.py b/test/ao/sparsity/test_composability.py
index b3aaf1c6dfbe..528fe9b83c65 100644
--- a/test/ao/sparsity/test_composability.py
+++ b/test/ao/sparsity/test_composability.py
@@ -411,7 +411,6 @@ class TestFxComposability(TestCase):
         )
         self.assertGreaterAlmostEqual(cur_sparsity, sparse_config[0]["sparsity_level"])
 
-    @xfailIfS390X
     def test_q_prep_fx_s_prep_ref_conv(self):
         r"""
         This checks that the ordering: prepare_fx -> sparse prepare -> convert_to_reference_fx
@@ -586,7 +585,6 @@ class TestFxComposability(TestCase):
         )
         self.assertGreaterAlmostEqual(cur_sparsity, sparse_config[0]["sparsity_level"])
 
-    @xfailIfS390X
     def test_s_prep_q_prep_fx_ref(self):
         r"""
         This checks that the ordering: sparse prepare -> prepare_fx -> convert_to_reference_fx
diff --git a/test/export/test_converter.py b/test/export/test_converter.py
index 9d872f87d60a..e739e5c34667 100644
--- a/test/export/test_converter.py
+++ b/test/export/test_converter.py
@@ -1448,7 +1448,11 @@ class TestConverter(TestCase):
             ep_out, _ = pytree.tree_flatten(ep.module()(*inp))
             self._check_tensor_list_equal(orig_out, ep_out)
 
-    # qnnpack not supported on s390x
+    # qnnpack/xnnpack not supported on s390x.
+    # it is required by
+    # torch.ops.prepacked.linear_clamp_prepack
+    # and
+    # torch.ops.prepacked.linear_clamp_run
     @xfailIfS390X
     def test_ts2ep_convert_quantized_model_with_opcontext(self):
         class M(torch.nn.Module):
@@ -1467,6 +1471,12 @@ class TestConverter(TestCase):
         inp = (torch.randn(1, 10),)
         self._check_equal_ts_ep_converter(m, inp, ["script"])
 
+    # qnnpack/xnnpack not supported on s390x.
+    # it is required by
+    # torch.ops.prepacked.linear_clamp_prepack
+    # and
+    # torch.ops.prepacked.linear_clamp_run
+    @xfailIfS390X
     def test_ts2ep_convert_quantized_model_with_opcontext_and_constant(self):
         class M(torch.nn.Module):
             def __init__(self, linear_op):
diff --git a/test/run_test.py b/test/run_test.py
index c0a61749936e..9af4e5ff5deb 100755
--- a/test/run_test.py
+++ b/test/run_test.py
@@ -185,28 +185,15 @@ S390X_BLOCKLIST = [
     "lazy/test_meta_kernel",
     "onnx/test_utility_funs",
     "profiler/test_profiler",
-    "test_ao_sparsity",
     "test_jit",
-    "test_metal",
-    "test_mps",
-    "dynamo/test_torchrec",
-    "inductor/test_aot_inductor_utils",
-    "inductor/test_coordinate_descent_tuner",
-    "test_jiterator",
-    "inductor/test_cpu_cpp_wrapper",
-    "export/test_converter",
-    "inductor/test_inductor_freezing",
     "dynamo/test_utils",
     "test_nn",
-    "functorch/test_ops",
     # these tests run long and fail in addition to that
     "dynamo/test_dynamic_shapes",
     "test_quantization",
     "inductor/test_torchinductor",
     "inductor/test_torchinductor_dynamic_shapes",
     "inductor/test_torchinductor_opinfo",
-    "test_binary_ufuncs",
-    "test_unary_ufuncs",
     # these tests fail when cuda is not available
     "inductor/test_aot_inductor",
     "inductor/test_best_config",
@@ -225,9 +212,12 @@ S390X_BLOCKLIST = [
     # these tests fail when mkldnn is not available
     "inductor/test_custom_post_grad_passes",
     "inductor/test_mkldnn_pattern_matcher",
+    "test_metal",
     # lacks quantization support
     "onnx/test_models_quantized_onnxruntime",
     "onnx/test_pytorch_onnx_onnxruntime",
+    # sysctl -n hw.memsize is not available
+    "test_mps",
     # https://github.com/pytorch/pytorch/issues/102078
     "test_decomp",
     # https://github.com/pytorch/pytorch/issues/146698
@@ -246,6 +236,9 @@ S390X_BLOCKLIST = [
     "inductor/test_config",
     "test_public_bindings",
     "test_testing",
+    # depend on z3-solver
+    "fx/test_z3_gradual_types",
+    "test_proxy_tensor",
 ]
 
 XPU_BLOCKLIST = [