The incremental energy loss ΔE/Eper unit path length for a boundary mode traveling along a rough surface may be calculated from elementary low‐frequency scattering approximations, using previously published results [I. Tolstoy, J. Acoust. Soc. Am.74, 1068–1070 (1983) and72, 960–972 (1982)]. This allows one to calculate explicitly the attenuation factor exp( − δr), whereris the range, withδ = 12ΔE/Efor rough two‐fluid interfaces with arbitrary impedances, constraints, and roughness shapes. It is shown that δ =Af6, wherefis the frequency andAa parameter which depends upon the size, spacing, and form of the roughness (for close‐packed roughness elementsAis proportional to the fifth power of the mean roughness height). Given a point source of sound and a receiver on the rough interface the boundary wave amplitudepB∝r−1/2f3/2exp( − δr) and exhibits, for fixedr, a well‐defined maximum in the frequency domain atfM= (4Ar)−1/6and falls off rapidly for higher frequencies, i.e., it displays a bandpass behavior with slow roll‐off at low frequencies. The predictions of this theory agree with recently reported model work [G.L.D'Spainet al., J. Acoust. Soc. Am., in press]. [Work supported by ONR.]