For an ocean sound channel whose environmental parameters depend not only on depth, but in a gradual fashion also on range, the wave equation may be separated by the adiabatic range variation method of Pierce [J. Acoust. Soc. Am. 37, 19 (1965)]. This method is used here to calculate underwater sound propagation in a channel with arbitrary (but gradual) range dependence, and also with arbitrary depth dependence of the sound velocity profile, by employing Airy function solutions of segmentwise linearized problems. Our results are illustrated for a realistic deep‐water propagation case with profile data collected in the western North Atlantic, as well as a shallow‐water example from the Norwegian Sea, and compared against the experimental transmission loss data, and the results of calculations using other methods for the same cases.