This research is to develop the theory and a computer code for readily available personal computers to calculate earthquake ground response for sites on the surface of a sediment-filled valley or basin. The fundamental objective is the theoretical determination of the eigenmodes (eigenfrequencies and eigenfunctions) of elastic waves in basins of arbitrary shape. With a judicious choice of approximations, this calculation could be readily available to a wide spectrum of users whereas current calculations require extensive codes and large computers for even simple basin structures. Applications are to site specific engineering and earthquake hazard estimations. This research is a component of the National Earthquake Hazard Reduction Program.