A dilator for use in accessing a vessel or other hollow organ is provided. The dilator has an extruded shaft with a tip portion at the distal end. The tip portion is formed by inserting the distal end portion of an extruded shaft into a die. Typically, the tip portion is molded to be tapered, and has a matte finish on at least a portion of its surface. The non-tapered shaft portion of the dilator may also have a matte finish that is typically formed during the extrusion process. In one embodiment, the matte surface is imparted to the surface of the tip portion after the shaft of the dilator has been extruded, by molding the tip portion in a die that has a matte or unpolished surface. The surface of the molded tip portion is then the inverse of the pattern on the surface of the die.