Two modelling approaches for the analyses of half-space and train-track embankment on half-space subjected to dynamic loads are presented and compared. A three-dimensional modelling approach is performed by a coupled Boundary Element - Boundary Element method (BE-BE) and a two-dimensional one by a coupled Boundary Element - Finite Element method (BE-FE). Both approaches employ time-domain algorithms. The comparison between the results of the presented approaches points out whether a problem can be treated as a two-dimensional or as a three-dimensional case. As an application, a parametric study of the wave propagation problem in a train-track embankment with an underlying half-space is presented.