Abstract: An intravenous catheter includes a tubular member made from a shrinkable material that has a built-in cutting tip located at its distal end. The cutting tip is adapted to cut through tissue and create an opening in a blood vessel of a patient that is the same diameter as the outer diameter of the tubular member. The tubular member is shrinkably affixed to at least a portion of the cutting tip to prevent removal of the cutting tip during usage or insertion. Another embodiment of the intravenous catheter includes a cutting tip disposed near the distal end of a tubular member tube and having a middle portion formed from a shrinkable material surrounding both the cutting tip and tubular member. The middle portion keeps the cutting tip and tubular member together and creates an integrated unit having a smooth outer surface and a continuous outer diameter throughout.