Starting from two-dimensional (2D) equations of motion and making use of the Galerkin weighted residual approximations, discretized formulations in the Laplace transform domain for the transient behavior of soil-structure interaction problems have been derived. Three different dynamic infinite elements taking into account single- and multiwave types are presented in the transformed space. By coupling the infinite elements with standard finite elements, an ordinary finite-element procedure is used for the simulation of wave propagation in an unbounded foundation due to the external forces. In this model, only source problems can be handled. Examples studied here indicate that the present approach has sufficient computational accuracy and feasibility for analyzing the transient response of complicated soil-structure interaction problems.