The interaction of ultrasound with rough surfaces is being actively investigated, from both a theoretical and experimental standpoint. The problem is important to several areas, including ocean acoustics [1,2] and dielectric waveguides, such as optical fibers. In either of these problems the fields can be assumed to be represented by a single scalar potential. The problem we address here has previously received very little attention, and concerns the propagation of guided elastic waves in a planar solid waveguide having randomly rough surfaces with compressional and shear potentials that are coupled at each interface. The rough surface is intended to model incipient corrosion in aluminum aircraft structure.