diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 4ef1fb8d63bb2e..c0e040d77253fe 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -42,6 +42,7 @@
 IS_LIBRESSL = ssl.OPENSSL_VERSION.startswith('LibreSSL')
 IS_OPENSSL_1_1_0 = not IS_LIBRESSL and ssl.OPENSSL_VERSION_INFO >= (1, 1, 0)
 IS_OPENSSL_1_1_1 = not IS_LIBRESSL and ssl.OPENSSL_VERSION_INFO >= (1, 1, 1)
+IS_OPENSSL_3_0_0 = not IS_LIBRESSL and ssl.OPENSSL_VERSION_INFO >= (3, 0, 0)
 PY_SSL_DEFAULT_CIPHERS = sysconfig.get_config_var('PY_SSL_DEFAULT_CIPHERS')
 
 PROTOCOL_TO_TLS_VERSION = {}
@@ -212,6 +213,10 @@ def has_tls_version(version):
     if not getattr(ssl, f'HAS_{version.name}'):
         return False
 
+    if IS_OPENSSL_3_0_0 and version < ssl.TLSVersion.TLSv1_2:
+        # bpo43791: 3.0.0-alpha14 fails with TLSV1_ALERT_INTERNAL_ERROR
+        return False
+
     # check runtime and dynamic crypto policy settings. A TLS version may
     # be compiled in but disabled by a policy or config option.
     ctx = ssl.SSLContext()
diff --git a/Misc/NEWS.d/next/Tests/2021-04-09-15-10-38.bpo-43791.4KxiXK.rst b/Misc/NEWS.d/next/Tests/2021-04-09-15-10-38.bpo-43791.4KxiXK.rst
new file mode 100644
index 00000000000000..964ae5abb3d880
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2021-04-09-15-10-38.bpo-43791.4KxiXK.rst
@@ -0,0 +1,2 @@
+OpenSSL 3.0.0: Disable testing of legacy protocols TLS 1.0 and 1.1. Tests
+are failing with TLSV1_ALERT_INTERNAL_ERROR.