In this paper, a new prediction methodology to deal with longitudinally invariant soil-structure interaction problems in elastodynamics is presented. The method uses the finite-element method to model the structure, the boundary-element method to model the local soil surrounding the structure and the method of fundamental solutions to model the wave propagation through the soil. All those methods are formulated in the two-and-a-half-dimensional domain. The methodology is firstly verified in the framework of a homogeneous half-space system by comparing the results of the current method with those computed by the semi-analytical solution of this problem. Secondly, the methodology is verified against a two-and-a-half-dimensional finite element-boundary element approach, for two calculation examples: a tunnel embedded in a homogeneous half-space and a tunnel embedded in a layered half-space. This comparison also shows that this novel methodology reduces the computational costs of such simulations without compromising the accuracy of the results. The increase on the computational efficiency is due to the use of the method of fundamental solutions to account for the wave propagation in the medium, and it is even higher when the number of evaluation points increases.