Asymptotic ray theory can be used to simulate acoustic waves in range‐dependent oceans, but singularities often occur at points of great interest. Transform methods, such as the WKBJ solution used by M.G. Brown [Ph.D. thesis, University of California, San Diego, CA (1982)], describe waves at the singular points, but they are restricted to laterally homogeneous media. Maslov asymptotic theory combines asymptotic ray theory and transform methods to provide a uniform result applicable in range‐dependent environments, and the technique was used by C. H. Chapman and R. Drummond [Bull. Seismol. Soc. Am.72(6), S217–S317 (December 1982)] to compute synthetic body‐wave seismograms. This paper describes a. computer simulation of underwater acoustic signals in range‐dependent oceans that is based upon Maslov asymptotic theory. The theory and computer implementation will be summarized, and examples will be discussed. Preliminary results on range‐dependent signal inversions for underwater acoustic tornography will also be presented.