A catheter has an entrance opening defined by the first end of a catheter body and non-circular inner surface in cross section. The entrance opening intersects a longitudinal axis extending longitudinally through the center of a lumen adapted to drain urine from a bladder. The non-circular inner surface can have dimples, channels, or grooves, all of which decrease frictional fluid forces against the inner surface as the urine drains. The catheter is free of any eyelets formed in the side wall of the catheter body. The catheter further includes a plurality of distinct longitudinally extending convex outer surfaces and may have an enlarged head.