Seismic analyses of concrete gravity dams are usually idealized as two-dimensional structures with a massless foundation in present design procedure. But for gravity dams built in narrow valleys or on sites of very high seismicity, however, interaction between adjacent blocks may influence the seismic responses significantly. Dynamic interaction between dam and foundation affects the dam response as well, including reflection, diffraction and radiation of seismic waves. In the paper, a three-dimensional FEM full dam model was adopted to analyze the seismic responses of a concrete gravity dam, in which, dynamic interaction between dam-foundation, dam-water, energy radiation, dynamic contact between monoliths, etc. were taken into consideration. Comparison was made among the numerical results of a full dam model with a massless foundation, full dam model with or without contraction joints, differences between them and realistic understanding were discussed and proposals were given to improve the aseismic capacity of concrete gravity dams.