diff --git a/testenv/test/base_test.py b/testenv/test/base_test.py
index 5e7126a4..3b989100 100644
--- a/testenv/test/base_test.py
+++ b/testenv/test/base_test.py
@@ -113,6 +113,7 @@ class BaseTest:
             cmd_line = 'valgrind --error-exitcode=301 ' \
                                 '--leak-check=yes ' \
                                 '--track-origins=yes ' \
+                                '--suppressions=../valgrind-suppression-ssl ' \
                                 '%s %s ' % (wget_path, wget_options)
         elif valgrind not in ("", "0"):
             cmd_line = '%s %s %s ' % (os.getenv("VALGRIND_TESTS", ""),
diff --git a/testenv/valgrind-suppression-ssl b/testenv/valgrind-suppression-ssl
new file mode 100644
index 00000000..02507850
--- /dev/null
+++ b/testenv/valgrind-suppression-ssl
@@ -0,0 +1,28 @@
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Cond
+   ...
+   obj:*/libcrypto.so.*
+}
+
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Cond
+   ...
+   obj:*/libssl.so.*
+}
+
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Value8
+   ...
+   obj:*/libcrypto.so.*
+}
+
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Param
+   write(buf)
+   ...
+   obj:*/libcrypto.so.*
+}
diff --git a/tests/Test-proxied-https-auth-keepalive.px b/tests/Test-proxied-https-auth-keepalive.px
index 349778a1..e407f315 100755
--- a/tests/Test-proxied-https-auth-keepalive.px
+++ b/tests/Test-proxied-https-auth-keepalive.px
@@ -150,7 +150,7 @@ my $valgrind = $ENV{VALGRIND_TESTS};
 if (!defined $valgrind || $valgrind eq "" || $valgrind == 0) {
     # Valgrind not requested - leave $cmdline as it is
 } elsif ($valgrind == 1) {
-    $cmdline = "valgrind --error-exitcode=301 --leak-check=yes --track-origins=yes " . $cmdline;
+    $cmdline = "valgrind --suppressions=valgrind-suppressions-ssl --error-exitcode=301 --leak-check=yes --track-origins=yes " . $cmdline;
 } else {
     $cmdline = $valgrind . " " . $cmdline;
 }
diff --git a/tests/Test-proxied-https-auth.px b/tests/Test-proxied-https-auth.px
index d2c710a3..1daefe83 100755
--- a/tests/Test-proxied-https-auth.px
+++ b/tests/Test-proxied-https-auth.px
@@ -149,7 +149,7 @@ my $valgrind = $ENV{VALGRIND_TESTS};
 if (!defined $valgrind || $valgrind eq "" || $valgrind == 0) {
     # Valgrind not requested - leave $cmdline as it is
 } elsif ($valgrind == 1) {
-    $cmdline = "valgrind --error-exitcode=301 --leak-check=yes --track-origins=yes " . $cmdline;
+    $cmdline = "valgrind  --suppressions=valgrind-suppressions-ssl --error-exitcode=301 --leak-check=yes --track-origins=yes " . $cmdline;
 } else {
     $cmdline = $valgrind . " " . $cmdline;
 }
diff --git a/tests/valgrind-suppressions-ssl b/tests/valgrind-suppressions-ssl
new file mode 100644
index 00000000..02507850
--- /dev/null
+++ b/tests/valgrind-suppressions-ssl
@@ -0,0 +1,28 @@
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Cond
+   ...
+   obj:*/libcrypto.so.*
+}
+
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Cond
+   ...
+   obj:*/libssl.so.*
+}
+
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Value8
+   ...
+   obj:*/libcrypto.so.*
+}
+
+{
+   <insert_a_suppression_name_here>
+   Memcheck:Param
+   write(buf)
+   ...
+   obj:*/libcrypto.so.*
+}