The present invention provides an apparatus and method for manufacturing polymeric thin-walled tubular members, which are well-suited for use as vascular grafts. The apparatus of the present invention enables extrusion of a tubular member having an extremely thin wall thickness so as to facilitate passage through tortuous vascular passageways. The apparatus achieves uniform wall thickness in a tubular member by establishing and maintaining axial alignment of a ram having a concentrically disposed guide rod therein with a die supported in concentric relation to the guide rod.