A plaque scoring catheter comprises a catheter body having a balloon or other radially expansible shell at its distal end. A non-axial scoring structure is carried over the shell and scores a stenosed region in a blood vessel when the balloon is inflated therein. The non-axial scoring structure may be formed directly on the balloon or may alternatively be part of a cage structure which floats over the balloon. Exemplary configurations for the scoring structure include helical, serpentine, and irregular.