The action of a plane wave upon a sinusoidal pressure‐release surface covering an impenetrable medium is studied by means of the Rayleigh and Waterman theories. It is demonstrated that solutions computed from the Rayleigh theory are obtained in about half the time necessary for the obtention of Waterman theory solutions having the same precision. Furthermore, it is possible to obtain solutions from the Rayleigh theory, at quite reasonable cost, that are at least as precise as those obtained from the integral equation method by Uretsky in connection with the experiments of La Casce and Tamarkin. This proves, contrary to prevailing opinion, that the Rayleigh theory is fully capable of describing the scattering phenomena produced by a wide class of corrugated surfaces, including those whose roughness is rather large. The minimal width of this class is shown herein to be 0