The weighted residual method was applied to the problem ofscattering and diffraction of plane elastic waves, in the form of antiplane waves, by a soft alluvial valley of arbitrary shape on the surface of a two-dimensional half-space. In order to demonstrate the versatility of the method, it was applied to shallow and deep circular, elliptical, and rectangular alluvial valleys. Results obtained are quite similar to those obtained using available closed form solutions. It was shown that significant ground motion amplitudes, with respect to the amplitude of incident waves, occurred on the ground surface of or near the alluvial valley. Amplitudes were dependent upon the shape and depth of the valley, the relative properties of the material in the valley and the surrounding medium, and the frequency and angle of incidence of incoming waves. Surface amplitude profiles for the lower frequency incident waves were simple near the discontinuity with peak amplitudes that did not vary much from 2 except on the surface of the alluvium. As the frequency of the incident waves was increased, the amplitude profiles near the valley became more complicated with peak values exceeding 5 on the surface of the half-space adjacent to the valley and exceeding 10 on the surface of the soft valley alluvium.