A cannula for insertion into a body cavity, duct, or vessel of a patient includes a parent cannula member and an integral radiopaque tip. The tip is configured so as to be distinguishable from internal body parts in an X ray or flouroscopic image, thus serving to precisely locate the position of the cannula within the patient without substantially obstructing the physician's view of such body parts. The cannula tip and parent member are separately pre-formed from a non-toxic polymeric material and can be constructed so as to have different hardnesses. In one embodiment, the tip is softer than the parent member in order to prevent internal injury to the patient, while in a second embodiment the tip is harder than the parent member for facilitating certain catheterization applications. The pre-formed tip and parent member are then dielectrically heated and welded securely together to form a unitary, integral cannula. The electrodes of the dielectric heating apparatus are connected to dies whose diametrical dimensions conform closely to those of the tip and parent member to provide the present cannula with completely smooth interior and exterior surfaces. In order to prevent the burning of the cannula during this heating process, air is vented from the junction area by providing the outer die with a convex interior surface and by forming longitudinal grooves in the external surface of the inner die or mandrel. The inner mandrel is formed by encapsulating the inner electrode with a highly insulative material to further inhibit burning of the cannula.