Apparatus for shaping a selected end region of a hollow cylindrical glass tube includes an internal mold placed within the selected end region for supporting the walls of the tube and controlling the shape of the internal surface of selected end region of the tube, during the period of time heat is applied to the tube and the tube is being shaped. In one embodiment the internal mold has a variable configuration and may be selectively set to an extended (open) configuration or to a collapsed (closed) configuration. With the internal mold set to its extended configuration, sufficient heat may be applied to the selected end region to render it malleable. Then, compression forces may be applied to the exterior surface of the tube to press the inner surface of the selected end region of the tube against the outer surface of the internal mold, causing the inner surface of the selected end region to conform to the outer surface of the internal mold. After the tube is shaped the internal mold may be set to its collapsed configuration and removed from the tube.