A method is presented which is useful for obtaining the scattered field due to a Love wave incident upon a local boundary irregularity in the elastic layer along which the wave is propagating. The problem is solved for the special case of a rigid half-space underlying the layer. The method uses a least squares procedure to approximately satisfy the traction-free boundary condition at the free surface irregularity and is shown to give good results for cases in which other approximate methods, such as a perturbation technique, are not accurate. Data from specific examples indicates the general range of applicability of the present approach. The method can be readily modified to handle acoustic waveguide problems of similar geometry and for various boundary conditions. In particular, with proper interpretation, the Love wave results presented herein directly apply to a specific acoustic waveguide with a local surface irregularity. The relationship of the present method to a previous work of another author concerned with the reflection of a plane wave (propagating in a half-space) from a periodically uneven surface is described.