The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, ?, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domain, and has errors that increase with azimuthal angle from the x axis. The cylindrical model has consistent validity in each azimuthal direction, but a fixed cylindrical grid of radials cannot produce uniform resolution. Two different methods to achieve more uniform resolution in the cylindrical PE model are presented. One of the methods is to increase the grid points in azimuth, as a function of r, according to nonaliased sampling theory. The other is to make use of a fixed arc-length grid. In addition, a point-source starter is derived for the three-dimensional Cartesian PE model. Results from idealized seamount and slope calculations are shown to compare and verify the performance of the three methods.