A study of the effects of dam-foundation interaction on the response of earth, rockfill and concrete-faced rockfill dams to obliquely incident P, SV and Rayleigh waves is presented. Emphasis is placed on the effects of the foundation flexibility, the spatial variability of the ground motion and the material nonlinearity. The study is based on a rigorous hybrid numerical formulation that combines the efficiency and versatility of the Finite Element Method (FEM) and the ability of Boundary Element Method (BEM) to account for the radiation conditions at the far field. The developed hybrid method is very powerful, and can be used efficiently to obtain accurate solutions of problems of complex geometry, material heterogeneity and, for time-domain analysis, material nonlinearity. The 2-D frequency-domain formulation is used at first to investigate the linear response of earth and rockfill dams to incident P, SV and Rayleigh waves and the response of concrete-faced rockfill dams to incident Rayleigh waves. Furthermore, the nonlinear time-domain coupled BE-FE formulation is used to investigate the response of earth and rockfill dams to vertically incident SV waves. By accounting rigorously for the energy radiated back into the halfspace, the study demonstrates the dramatic effect of the flexibility of the foundation rock in reducing the overall response of the dam. The effects of the spatial variability of the ground motion across the width of the dam are also shown to be important, but less dramatic than those of the foundation flexibility. Finally, the results from the nonlinear analysis of two different dams, each experiencing various degrees of nonlinearity, have demonstrated the great importance of the material nonlinear behavior on the response of dams subjected to strong ground motion.