Dynamics of railway tracks have been studied for a long time. Many authors proposed analytical or numerical models to compute the dynamic response of the tracks. Numerical models often use the track periodicity to reduce the size of the problem. Among these numerical methods, the Wave Finite Element (WFE) method was designed to compute the dynamics of periodic structures composed of identical patterns. It was successfully applied to simplied models of railway tracks subjected to dierent types of loads. In these studies, tracks are modeled by periodically supported beams. In order to give access to stresses and strains at a ne scale, a much ner representation is needed. This article presents a WFE computation of the dynamics of a ballastless railway track subjected to constant moving loads. In the presented computation the rail, the underlying slab and the support system are all represented in three dimensions. In order to validate this method, the obtained results are compared to experimental strain measurements.