Scattering by inhomogeneities in homogeneous media can be analyzed in an elegant manner by reducing the problem statement to the solution of a system of singular integral equations over the surface of the scatterer [1]. This system can be solved in a relatively straight forward manner by the use of the boundary element method [2]. An inhomogeneity in an interface between two solids of different mechanical properties presents some additional complications to the numerical analyst. These complications are discussed in this paper. In deriving the system of singular integral equations, it was decided to use the Green’s functions for the unbounded regions of the two materials, rather than the single Green’s function for the space of the joined half spaces. This approach introduces a considerable simplification in the integrands, but at the expense of the addition of a set of boundary integral equations over the interface between the two solids, outside of the inhomogeneity. In the boundary element approach the domain of these equations has to be truncated. Specific results are presented for backscattering by a spherical cavity in the interface of solids of different elastic moduli and mass densities.