diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index a9d93f473e0e1..2ef9e4a028793 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1286,16 +1286,18 @@ def _format_native_types(self, na_rep="nan", **kwargs):
 
         # go through the levels and format them
         for level, level_codes in zip(self.levels, self.codes):
-            level = level._format_native_types(na_rep=na_rep, **kwargs)
+            level_strs = level._format_native_types(na_rep=na_rep, **kwargs)
             # add nan values, if there are any
             mask = level_codes == -1
             if mask.any():
-                nan_index = len(level)
-                level = np.append(level, na_rep)
+                nan_index = len(level_strs)
+                # numpy 1.21 deprecated implicit string casting
+                level_strs = level_strs.astype(str)
+                level_strs = np.append(level_strs, na_rep)
                 assert not level_codes.flags.writeable  # i.e. copy is needed
                 level_codes = level_codes.copy()  # make writeable
                 level_codes[mask] = nan_index
-            new_levels.append(level)
+            new_levels.append(level_strs)
             new_codes.append(level_codes)
 
         if len(new_levels) == 1:
diff --git a/pandas/tests/indexes/test_numeric.py b/pandas/tests/indexes/test_numeric.py
index ff1632e33c0fb..d12e9465949b4 100644
--- a/pandas/tests/indexes/test_numeric.py
+++ b/pandas/tests/indexes/test_numeric.py
@@ -204,12 +204,17 @@ def test_constructor_invalid(self):
         )
         with pytest.raises(TypeError, match=msg):
             Float64Index(0.0)
-        msg = (
-            "String dtype not supported, "
-            "you may need to explicitly cast to a numeric type"
+
+        # 2021-02-1 we get ValueError in numpy 1.20, but not on all builds
+        msg = "|".join(
+            [
+                "String dtype not supported, you may need to explicitly cast ",
+                "could not convert string to float: 'a'",
+            ]
         )
-        with pytest.raises(TypeError, match=msg):
+        with pytest.raises((TypeError, ValueError), match=msg):
             Float64Index(["a", "b", 0.0])
+
         msg = r"float\(\) argument must be a string or a number, not 'Timestamp'"
         with pytest.raises(TypeError, match=msg):
             Float64Index([Timestamp("20130101")])
diff --git a/pandas/tests/tseries/offsets/test_offsets_properties.py b/pandas/tests/tseries/offsets/test_offsets_properties.py
index 8d9b54cf3f0df..edb0f8c7dd662 100644
--- a/pandas/tests/tseries/offsets/test_offsets_properties.py
+++ b/pandas/tests/tseries/offsets/test_offsets_properties.py
@@ -10,6 +10,7 @@
 import warnings
 
 from hypothesis import assume, given, strategies as st
+from hypothesis.errors import Flaky
 from hypothesis.extra.dateutil import timezones as dateutil_timezones
 from hypothesis.extra.pytz import timezones as pytz_timezones
 import pytest
@@ -103,6 +104,7 @@ def test_on_offset_implementations(dt, offset):
     assert offset.is_on_offset(dt) == (compare == dt)
 
 
+@pytest.mark.xfail(strict=False, raises=Flaky, reason="unreliable test timings")
 @given(gen_yqm_offset)
 def test_shift_across_dst(offset):
     # GH#18319 check that 1) timezone is correctly normalized and