A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil}structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the e!ects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary "nite-element method, is used and the structure is modelled by 8}21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to e$cient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary "nite-element method resulting in signi"cant reduction in computational e!ort with little loss of accuracy. The approximations also lead to a very e$cient scheme for evaluation of convolution integrals in the calculation of soil}structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil}Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil}structure interaction as well as in the analysis of wave scattering and di!raction by three-dimensional surface irregularities. The scattering and di!raction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very e$cient for problems which involve low frequencies of interest for earthquake engineering.