Accurate numerical solutions generated with a new computational model are presented for several range‐dependent underwater acoustic problems involving penetrable ocean bottoms. The multifilament source model [Boagetal., ‘‘Analysis of acoustic scattering from fluid cylinders using a multifilament source model,’’ J. Acoust. Soc. Am.83, 1–8 (1988)], originally developed to treat acoustic scattering by arbitrarily shaped cylinders embedded in an infinite medium, has been extended to solve short‐range ocean acoustic problems. Source model solutions for two different range‐dependent problems agree with solutions that were obtained with Evans’ COUPLE model [R. B. Evans, ‘‘A coupled mode solution for acoustic propagation in a waveguide with stepwise depth variations of a penetrable bottom,’’ J. Acoust. Soc. Am.74, 188–195 (1983)]. These comparisons demonstrate the source model’s ability to describe propagation in a shallow water environment with rapidly varying bathymetry and a lossy, penetrable bottom.