diff --git a/numpy/core/tests/test_umath.py b/numpy/core/tests/test_umath.py
index c0b26e75b2c8..e7fee46b7b79 100644
--- a/numpy/core/tests/test_umath.py
+++ b/numpy/core/tests/test_umath.py
@@ -17,18 +17,8 @@
     assert_array_max_ulp, assert_allclose, assert_no_warnings, suppress_warnings,
     _gen_alignment_data, assert_array_almost_equal_nulp
     )
+from numpy.testing._private.utils import _glibc_older_than
 
-def get_glibc_version():
-    try:
-        ver = os.confstr('CS_GNU_LIBC_VERSION').rsplit(' ')[1]
-    except Exception as inst:
-        ver = '0.0'
-
-    return ver
-
-
-glibcver = get_glibc_version()
-glibc_older_than = lambda x: (glibcver != '0.0' and glibcver < x)
 
 def on_powerpc():
     """ True if we are running on a Power PC platform."""
@@ -1014,7 +1004,7 @@ def test_exp_values(self):
 
     # See: https://github.com/numpy/numpy/issues/19192
     @pytest.mark.xfail(
-        glibc_older_than("2.17"),
+        _glibc_older_than("2.17"),
         reason="Older glibc versions may not raise appropriate FP exceptions"
     )
     def test_exp_exceptions(self):
@@ -1262,6 +1252,11 @@ def test_arctanh(self):
                     assert_raises(FloatingPointError, np.arctanh,
                                   np.array(value, dtype=dt))
 
+    # See: https://github.com/numpy/numpy/issues/20448
+    @pytest.mark.xfail(
+        _glibc_older_than("2.17"),
+        reason="Older glibc versions may not raise appropriate FP exceptions"
+    )
     def test_exp2(self):
         with np.errstate(all='ignore'):
             in_ = [np.nan, -np.nan, np.inf, -np.inf]
@@ -1397,7 +1392,7 @@ def test_sincos_float32(self):
         M = np.int_(N/20)
         index = np.random.randint(low=0, high=N, size=M)
         x_f32 = np.float32(np.random.uniform(low=-100.,high=100.,size=N))
-        if not glibc_older_than("2.17"):
+        if not _glibc_older_than("2.17"):
             # test coverage for elements > 117435.992f for which glibc is used
             # this is known to be problematic on old glibc, so skip it there
             x_f32[index] = np.float32(10E+10*np.random.rand(M))
diff --git a/numpy/core/tests/test_umath_accuracy.py b/numpy/core/tests/test_umath_accuracy.py
index 32e2dca66151..3d4d5b5aadc2 100644
--- a/numpy/core/tests/test_umath_accuracy.py
+++ b/numpy/core/tests/test_umath_accuracy.py
@@ -5,11 +5,14 @@
 import pytest
 from ctypes import c_longlong, c_double, c_float, c_int, cast, pointer, POINTER
 from numpy.testing import assert_array_max_ulp
+from numpy.testing._private.utils import _glibc_older_than
 from numpy.core._multiarray_umath import __cpu_features__
 
 IS_AVX = __cpu_features__.get('AVX512F', False) or \
         (__cpu_features__.get('FMA3', False) and __cpu_features__.get('AVX2', False))
-runtest = sys.platform.startswith('linux') and IS_AVX
+# only run on linux with AVX, also avoid old glibc (numpy/numpy#20448).
+runtest = (sys.platform.startswith('linux')
+           and IS_AVX and not _glibc_older_than("2.17"))
 platform_skip = pytest.mark.skipif(not runtest,
                                    reason="avoid testing inconsistent platform "
                                    "library implementations")
diff --git a/numpy/testing/_private/utils.py b/numpy/testing/_private/utils.py
index 0eb945d15cc7..2c71e45bdfa6 100644
--- a/numpy/testing/_private/utils.py
+++ b/numpy/testing/_private/utils.py
@@ -2518,3 +2518,16 @@ def wrapper(*args, **kwargs):
             finally:
                 sys.settrace(original_trace)
         return wrapper
+
+
+def _get_glibc_version():
+    try:
+        ver = os.confstr('CS_GNU_LIBC_VERSION').rsplit(' ')[1]
+    except Exception as inst:
+        ver = '0.0'
+
+    return ver
+
+
+_glibcver = _get_glibc_version()
+_glibc_older_than = lambda x: (_glibcver != '0.0' and _glibcver < x)