diff --git a/test/parallel/test-crypto.js b/test/parallel/test-crypto.js
index 76164c683f9e56..711280d09d0fe6 100644
--- a/test/parallel/test-crypto.js
+++ b/test/parallel/test-crypto.js
@@ -238,7 +238,7 @@ assert.throws(function() {
   // Throws crypto error, so there is an opensslErrorStack property.
   // The openSSL stack should have content.
   if ((err instanceof Error) &&
-      /asn1 encoding routines:ASN1_CHECK_TLEN:wrong tag/.test(err) &&
+      /asn1 encoding routines:[^:]*:wrong tag/.test(err) &&
       err.opensslErrorStack !== undefined &&
       Array.isArray(err.opensslErrorStack) &&
       err.opensslErrorStack.length > 0) {
diff --git a/test/parallel/test-tls-junk-server.js b/test/parallel/test-tls-junk-server.js
index 3270dec745c1ba..27c273857b51ff 100644
--- a/test/parallel/test-tls-junk-server.js
+++ b/test/parallel/test-tls-junk-server.js
@@ -21,7 +21,9 @@ server.listen(0, function() {
   req.end();
 
   req.once('error', common.mustCall(function(err) {
-    assert(/unknown protocol/.test(err.message));
+    // OpenSSL 1.0.x and 1.1.x use different error messages for junk inputs.
+    assert(/unknown protocol/.test(err.message) ||
+           /wrong version number/.test(err.message));
     server.close();
   }));
 });
diff --git a/test/parallel/test-tls-no-sslv3.js b/test/parallel/test-tls-no-sslv3.js
index 9622262f38cbf3..aa37fc2e3b64fa 100644
--- a/test/parallel/test-tls-no-sslv3.js
+++ b/test/parallel/test-tls-no-sslv3.js
@@ -46,6 +46,8 @@ process.on('exit', function() {
     common.printSkipMessage('`openssl s_client -ssl3` not supported.');
   } else {
     assert.strictEqual(errors.length, 1);
-    assert(/:wrong version number/.test(errors[0].message));
+    // OpenSSL 1.0.x and 1.1.x report invalid client versions differently.
+    assert(/:wrong version number/.test(errors[0].message) ||
+           /:version too low/.test(errors[0].message));
   }
 });
diff --git a/test/parallel/test-tls-server-failed-handshake-emits-clienterror.js b/test/parallel/test-tls-server-failed-handshake-emits-clienterror.js
index 8efb4ec53866d5..c4351008c147c9 100644
--- a/test/parallel/test-tls-server-failed-handshake-emits-clienterror.js
+++ b/test/parallel/test-tls-server-failed-handshake-emits-clienterror.js
@@ -20,8 +20,10 @@ const server = tls.createServer({})
   }).on('tlsClientError', common.mustCall(function(e) {
     assert.ok(e instanceof Error,
               'Instance of Error should be passed to error handler');
+    // OpenSSL 1.0.x and 1.1.x use different error codes for junk inputs.
     assert.ok(
-      /SSL routines:SSL23_GET_CLIENT_HELLO:unknown protocol/.test(e.message),
+      /SSL routines:[^:]*:(unknown protocol|wrong version number)/.test(
+        e.message),
       'Expecting SSL unknown protocol');
 
     server.close();
diff --git a/test/parallel/test-tls-socket-failed-handshake-emits-error.js b/test/parallel/test-tls-socket-failed-handshake-emits-error.js
index a54b7170f08277..d67a5498d65195 100644
--- a/test/parallel/test-tls-socket-failed-handshake-emits-error.js
+++ b/test/parallel/test-tls-socket-failed-handshake-emits-error.js
@@ -20,8 +20,10 @@ const server = net.createServer(function(c) {
     s.on('error', common.mustCall(function(e) {
       assert.ok(e instanceof Error,
                 'Instance of Error should be passed to error handler');
+      // OpenSSL 1.0.x and 1.1.x use different error codes for junk inputs.
       assert.ok(
-        /SSL routines:SSL23_GET_CLIENT_HELLO:unknown protocol/.test(e.message),
+        /SSL routines:[^:]*:(unknown protocol|wrong version number)/.test(
+          e.message),
         'Expecting SSL unknown protocol');
     }));