In this paper, we report on some computational experience in solving ocean acoustic propagation problems in three dimensions on supercomputers. The underlying Helmholtz equation is transformed into a parabolic-type equation in the Lee-Saad-Schultz model [5], which has a natural alternating direction implicit (ADI) implementation. We give estimates of the computing power required to solve problems with realistic sound velocity profiles. We then give performance results for the CRAY X-MP and for the computational kernel on the Intel hypercube (iPSC/2). We conclude with some remarks about architectural enhancements that would be beneficial to our application.