A fencing construction made of thermoplastic materials which can be easily assembled utilizing ultrasonic welding and which can include a unique configuration for the ultrasonic welding surfaces which prevents the flow of melted thermoplastic materials outwardly onto the decorative outer surfaces of the various fencing parts. Any excess thermoplastic material is designed to pass inwardly toward the longitudinally extending bore defined in the various fencing construction parts. This concept is particularly useful for attaching capping fence members which are injection molded onto structural fence members which are extruded.