The problem of the scattering of acoustic waves by a large, sound soft (hard), corrugated surface in two dimensions is addressed. The surface undulates periodically up to a characteristic lengthLbeyond which it becomes planar. The height of the corrugation is measured by a characteristic length a and its period by Λ. The ordering of these scales is taken to be λ ∼ Λ ∼a⋘L, where λ is the wavelength of the incident plane acoustic wave. The method of matched asymptotic expansions is applied to analyze this problem in the limit as ε =a/L→0. This approach is both mathematically systematic and physically intuitive. The farfield results are identical to those obtained by using a finite beam approximation for a sound hard surface in two dimensions and almost the same for a sound soft case; the only difference being a sine factor that yields correct boundary behavior. Results are derived for the three‐dimensional scattering problems and these compare similarly. [Work supported by NSF and AFOSR.]