The full‐wave solution to the problem of acoustic surface‐wave scattering on a homogeneous isotropic three‐quarter space of Poisson's ratio &sgr;=0.245 has been obtained by a finite‐difference iterative method. The amplitude coefficients for Rayleigh wave transmission and reflection at the 270° corner were found to be 0.28±0.02 and 0.09±0.01, respectively, while the corresponding phase shifts were 140±10° and −125±10°. All of these results, which are independent of wavelength, agree well with previously published experimental and theoretical work. About 90% of the incident energy is lost to body waves and the scattered energy‐density pattern indicates that over half of this energy sweeps past the corner and propagates into the body of the medium in the form of bulk modes. Some of the incident energy tends to follow the free surface by swinging around the corner while the reflected wave appears to be launched mainly by the action of a virtual source located at the corner which is excited by the incoming wave and radiates into the three‐quarter space. The accuracy of the finite‐difference technique has also been verified by comparing the iterated results for Rayleigh wave propagation on a homogeneous isotropic semi‐infinite half‐space with the analytically exact results. This basic method may be extended to solve problems involving layered geometries.