diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index 48a6369b7a..91cc5b61b9 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -6370,6 +6370,12 @@ static uint16_t ssl_preset_default_sig_algs[] = {
     MBEDTLS_TLS13_SIG_ECDSA_SECP521R1_SHA512,
 #endif /* MBEDTLS_SHA512_C && MBEDTLS_ECP_DP_SECP521R1_ENABLED */
 #endif /* MBEDTLS_ECDSA_C */
+
+    /* RSA algorithms */
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
+    MBEDTLS_TLS13_SIG_RSA_PSS_RSAE_SHA256,
+#endif
+
     MBEDTLS_TLS13_SIG_NONE
 };
 
@@ -6383,6 +6389,12 @@ static uint16_t ssl_preset_suiteb_sig_algs[] = {
     MBEDTLS_TLS13_SIG_ECDSA_SECP384R1_SHA384,
 #endif /* MBEDTLS_SHA512_C && MBEDTLS_ECP_DP_SECP384R1_ENABLED */
 #endif /* MBEDTLS_ECDSA_C */
+
+    /* RSA algorithms */
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
+    MBEDTLS_TLS13_SIG_RSA_PSS_RSAE_SHA256,
+#endif
+
     MBEDTLS_TLS13_SIG_NONE
 };
 #endif /* MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL */
diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index 12ef4d58c8..6b7a6f84af 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -320,6 +320,11 @@ static int ssl_tls13_parse_certificate_verify( mbedtls_ssl_context *ssl,
     unsigned char verify_hash[MBEDTLS_MD_MAX_SIZE];
     size_t verify_hash_len;
 
+    void const *opts_ptr = NULL;
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
+    mbedtls_pk_rsassa_pss_options opts;
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT */
+
     /*
      * struct {
      *     SignatureScheme algorithm;
@@ -368,6 +373,13 @@ static int ssl_tls13_parse_certificate_verify( mbedtls_ssl_context *ssl,
             md_alg = MBEDTLS_MD_SHA512;
             sig_alg = MBEDTLS_PK_ECDSA;
             break;
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
+        case MBEDTLS_TLS13_SIG_RSA_PSS_RSAE_SHA256:
+            MBEDTLS_SSL_DEBUG_MSG( 4, ( "Certificate Verify: using RSA" ) );
+            md_alg = MBEDTLS_MD_SHA256;
+            sig_alg = MBEDTLS_PK_RSASSA_PSS;
+            break;
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT */
         default:
             MBEDTLS_SSL_DEBUG_MSG( 1, ( "Certificate Verify: Unknown signature algorithm." ) );
             goto error;
@@ -426,8 +438,21 @@ static int ssl_tls13_parse_certificate_verify( mbedtls_ssl_context *ssl,
     }
 
     MBEDTLS_SSL_DEBUG_BUF( 3, "verify hash", verify_hash, verify_hash_len );
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
+    if( sig_alg == MBEDTLS_PK_RSASSA_PSS )
+    {
+        const mbedtls_md_info_t* md_info;
+        opts.mgf1_hash_id = md_alg;
+        if( ( md_info = mbedtls_md_info_from_type( md_alg ) ) == NULL )
+        {
+            return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+        }
+        opts.expected_salt_len = mbedtls_md_get_size( md_info );
+        opts_ptr = (const void*) &opts;
+    }
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT */
 
-    if( ( ret = mbedtls_pk_verify_ext( sig_alg, NULL,
+    if( ( ret = mbedtls_pk_verify_ext( sig_alg, opts_ptr,
                                        &ssl->session_negotiate->peer_cert->pk,
                                        md_alg, verify_hash, verify_hash_len,
                                        p, signature_len ) ) == 0 )
diff --git a/programs/ssl/ssl_client2.c b/programs/ssl/ssl_client2.c
index cb299b159e..204b9754aa 100644
--- a/programs/ssl/ssl_client2.c
+++ b/programs/ssl/ssl_client2.c
@@ -1534,6 +1534,10 @@ int main( int argc, char *argv[] )
             {
                 sig_alg_list[i++] = MBEDTLS_TLS13_SIG_ECDSA_SECP521R1_SHA512;
             }
+            else if( strcmp( q, "rsa_pss_rsae_sha256" ) == 0 )
+            {
+                sig_alg_list[i++] = MBEDTLS_TLS13_SIG_RSA_PSS_RSAE_SHA256;
+            }
             else
             {
                 mbedtls_printf( "unknown signature algorithm %s\n", q );
@@ -1541,6 +1545,7 @@ int main( int argc, char *argv[] )
                 mbedtls_printf( "ecdsa_secp256r1_sha256 " );
                 mbedtls_printf( "ecdsa_secp384r1_sha384 " );
                 mbedtls_printf( "ecdsa_secp521r1_sha512 " );
+                mbedtls_printf( "rsa_pss_rsae_sha256 " );
                 mbedtls_printf( "\n" );
                 goto exit;
             }
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 1ac34dae77..d43d66260e 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -79,16 +79,20 @@ fi
 
 if [ -n "${OPENSSL_NEXT:-}" ]; then
     O_NEXT_SRV="$OPENSSL_NEXT s_server -www -cert data_files/server5.crt -key data_files/server5.key"
+    O_NEXT_SRV_RSA="$OPENSSL_NEXT s_server -www -cert data_files/server2-sha256.crt -key data_files/server2.key"
     O_NEXT_CLI="echo 'GET / HTTP/1.0' | $OPENSSL_NEXT s_client"
 else
     O_NEXT_SRV=false
+    O_NEXT_SRV_RSA=false
     O_NEXT_CLI=false
 fi
 
 if [ -n "${GNUTLS_NEXT_SERV:-}" ]; then
     G_NEXT_SRV="$GNUTLS_NEXT_SERV --x509certfile data_files/server5.crt --x509keyfile data_files/server5.key"
+    G_NEXT_SRV_RSA="$GNUTLS_NEXT_SERV --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key"
 else
     G_NEXT_SRV=false
+    G_NEXT_SRV_RSA=false
 fi
 
 if [ -n "${GNUTLS_NEXT_CLI:-}" ]; then
@@ -264,7 +268,7 @@ requires_config_value_equals() {
 # Space-separated list of ciphersuites supported by this build of
 # Mbed TLS.
 P_CIPHERSUITES=" $($P_CLI --help 2>/dev/null |
-                   grep TLS- |
+                   grep 'TLS-\|TLS1-3' |
                    tr -s ' \n' ' ')"
 requires_ciphersuite_enabled() {
     case $P_CIPHERSUITES in
@@ -1416,11 +1420,13 @@ fi
 
 if [ -n "${OPENSSL_NEXT:-}" ]; then
     O_NEXT_SRV="$O_NEXT_SRV -accept $SRV_PORT"
+    O_NEXT_SRV_RSA="$O_NEXT_SRV_RSA -accept $SRV_PORT"
     O_NEXT_CLI="$O_NEXT_CLI -connect 127.0.0.1:+SRV_PORT"
 fi
 
 if [ -n "${GNUTLS_NEXT_SERV:-}" ]; then
     G_NEXT_SRV="$G_NEXT_SRV -p $SRV_PORT"
+    G_NEXT_SRV_RSA="$G_NEXT_SRV_RSA -p $SRV_PORT"
 fi
 
 if [ -n "${GNUTLS_NEXT_CLI:-}" ]; then
@@ -8835,6 +8841,22 @@ run_test    "TLS1.3: minimal feature sets - openssl" \
             -c "<= parse finished message" \
             -c "HTTP/1.0 200 ok"
 
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_X509_RSASSA_PSS_SUPPORT
+requires_config_disabled MBEDTLS_USE_PSA_CRYPTO
+run_test    "TLS 1.3 m->O AES_128_GCM_SHA256      , RSA_PSS_RSAE_SHA256" \
+            "$O_NEXT_SRV_RSA -ciphersuites TLS_AES_128_GCM_SHA256 -tls1_3 -msg -no_middlebox -num_tickets 0" \
+            "$P_CLI debug_level=4 force_version=tls1_3 server_name=localhost force_ciphersuite=TLS1-3-AES-128-GCM-SHA256 allow_sha1=0" \
+            0 \
+            -c "ECDH curve: x25519" \
+            -c "server hello, chosen ciphersuite: ( 1301 ) - TLS1-3-AES-128-GCM-SHA256" \
+            -c "Certificate Verify: Signature algorithm ( 0804 )" \
+            -c "mbedtls_ssl_tls13_process_certificate_verify() returned 0" \
+            -c "HTTP/1.0 200 ok"
+
 requires_gnutls_tls1_3
 requires_gnutls_next_no_ticket
 requires_gnutls_next_disable_tls13_compat
@@ -8867,6 +8889,23 @@ run_test    "TLS1.3: minimal feature sets - gnutls" \
             -c "<= parse finished message" \
             -c "HTTP/1.0 200 OK"
 
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_X509_RSASSA_PSS_SUPPORT
+requires_config_disabled MBEDTLS_USE_PSA_CRYPTO
+requires_gnutls_next
+run_test    "TLS 1.3 m->G AES_128_GCM_SHA256      , RSA_PSS_RSAE_SHA256" \
+            "$G_NEXT_SRV_RSA --disable-client-cert --priority=NORMAL:+CIPHER-ALL:+SHA256:+GROUP-SECP256R1:+ECDHE-ECDSA:+AEAD:+SIGN-RSA-PSS-RSAE-SHA256:-VERS-ALL:+VERS-TLS1.3:%NO_TICKETS:%DISABLE_TLS13_COMPAT_MODE" \
+            "$P_CLI debug_level=4 force_version=tls1_3 server_name=localhost force_ciphersuite=TLS1-3-AES-128-GCM-SHA256 allow_sha1=0" \
+            0 \
+            -c "ECDH curve: x25519"         \
+            -c "server hello, chosen ciphersuite: ( 1301 ) - TLS1-3-AES-128-GCM-SHA256" \
+            -c "Certificate Verify: Signature algorithm ( 0804 )" \
+            -c "mbedtls_ssl_tls13_process_certificate_verify() returned 0" \
+            -c "HTTP/1.0 200 OK"
 
 # Test heap memory usage after handshake
 requires_config_enabled MBEDTLS_MEMORY_DEBUG