In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element-Boundary-Element technique (FE-BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil-structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as damfoundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam-foundation interaction.