Disclosed herein shock wave catheters comprising one or more shock wave electrodes for cracking calcifications located within blood vessels. In some variations, a shock wave catheter has first and second shock wave electrodes each circumferentially disposed over the outer surface of the catheter. In certain variations, the first electrode has a recess and the second electrode has a protrusion that is received by the recess and a spark gap is located along the separation between the recess and the protrusion. The second electrode can also have a recess that receives a protrusion from a third shock wave electrode, where the separation between the second and third electrodes along the separation between the recess and the protrusion forms a second spark gap. A shock wave can be initiated across these spark gaps when a voltage is applied over the electrodes.
