Using the governing differential equations of wave propagation problems and making use of the Galerkin weighted residual method, discretized formulations in the Laplace transform domain for the transient behaviour of unbounded domain problems have been presented for linear elastic and visco-elastic foundations. In this paper, two infinite elements, harmonic and transient, are presented. These elements are capable of considering three different wave types simultaneously. Examples considered in this study indicate that present formulations have sufficient computational accuracy for the solution of the transient and harmonic response of unbounded media problems. (C) 1999 Elsevier Science Ltd. All rights reserved.