Normal‐mode theory is applied to the problem of finding the variation of acoustic intensity with range in shallow water of variable depth. A solution of the wave equation is obtained by neglecting the coupling of normal modes produced by the horizontal variation of depth. Relatively simple formulas for the intensity as a function of range are obtained in the case of isovelocity water by averaging the expression for intensity over source and receiver positions and replacing a Summation over all the allowed modes by an integration at intermediate ranges. At long ranges, only the first mode is effective and a modified cylindrical spreading law is obtained.