A plane sound wave is assumed to be incident upon an irregular pressure release surfacez=ζ (x,y). The solution for the reflected field is regarded as a superposition of plane waves having an amplitude spectrumA(k1,k2). Next, the Fourier transformG(x,y) ofA(k1,k2) is introduced and subjected to the boundary condition on ζ This leads to an integral equation forG(x,y) that cannot be readily solved. However, if one causesG(x,y) to depend exponentially on a functionu(x,y), then a differential equation may be derived from this integral equation, the solution of which gives an approximate form ofu(x,y); the degree of approximation involved depends on the smallness of ζ.This method is applied to the problem of sound scattering from a one‐dimensional sinusoidally corrugated surface and the results compared with experimental measurements of LaCasce and Tamarkin and also with the results of a theory due to Rayleigh. This comparison shows the predictions of the theory presented here to be as good as the Rayleigh theory in all cases and closer in the majority of cases.