The concept of substructure deletion proposed for the analysis of a rigid embedded foundation was adapted for the analysis of site amplification effects in alluvial valleys. A major modification was made for the present application such that the boundary integration equation method was used for both the finite size interior problem and semi-infinite exterior wave radiation problem. The modification was made to reduce the possible incompatibility between the finite element method, a volume formulation, and the boundary integral equation method, a surface formulation. The substructure deletion concept allows simple, century-old, basic Green?s Functions to be used to produce excellent wave scattering results for topographical irregularities as well as arbitrarily shaped alluvial valleys overlying a stiffer bedrock. The concept is applicable to three dimensional geometries as well as two-dimensional problems. Results are given for incident SH, P, SV and Rayleigh waves.