This paper presents application to the soil-structure interaction problems of the three-dimensional time domain boundary element method (BEM). The contents are as follows: First, we show the fundamental solution and the boundary integral equation, and investigate the characteristics of the fundamental solution and the surface of discontinuity (wave front). Second, in the present work, constant boundary elements are used for discretization in space and linear elements for displacements variations in time are used. The step-by-step integration scheme is introduced in the implicit form. Third, in order to verify validity of the present method, we compare with the results of Dominguez and Karabalis. Through the comparisons, we refer to some questions on Karabalis' formulation. Finally, we perform parametric studies for the two foundations which are an embedded rigid foundation and a surface one. In particular, we wish to emphasize the importance of effects of the azimuth angles on the foundation input motions. As the conclusion, the soil-structure interaction problems can be analyzed effectively by using the present method.