An alternate formulation of the 'substructure deletion method' suggested by Dasgupta in 1979l has been successfully implemented. The idea is to utilize simple Green's functions developed for a surface problem to replace the more complicated Green's functions required for embedded problems while still being able to generate an accurate solution. Since the exterior medium is usually represented by a continuum model, the interior medium in the present approach will also be represented by a continuum model rather than a finite element model as suggested originally, thereby eliminating the incompatibility between the solutions of the interior and exterior media. Detailed studies of the method's accuracy and limitations were performed using two-dimensional examples in wave scattering of canyons and alluvial valleys, problems which are more suitable for this method than the embedded foundation problem. The results obtained indicate that the alternate formulation gives accurate results only when the vertical dimension of the scattering object is not too large; if the aspect ratio (vertical over lateral) exceeds a certain limit, the results will not approach the known results given by boundary integral equation solutions or indirect boundary integral equations no matter what the refinement of the model may be. The greatest advantage of the present method is that the task of calculating Green's functions is reduced significantly; computational time using this new formulation is approximately five times less than for conventional boundary integral equation methods.