Dynamic analysis of ground due to moving loads of rail traffic is important in design of railways. Indeed, the analysis can be useful for engineers to calculate and predict deterioration of railways, under moving loads. To model the soil-structure interaction, a semi-analytical model is presented in this study to model both the dynamic behavior of the railway track and the soil medium. This work deals with a semi-analytical analysis of wave propagation in the ground due to a moving harmonic load. The system is composed of a track coupled with a multilayered poroviscoelastic soil. The approach is proposed for a 3D modeling of railway/porous medium. It allows calculate through semi-analytical approach speed waves and displacements of each solid or fluid phase at any point of the soil in both wave numbers and space domains. A model using a beam incorporating all track components (rails, pads, sleepers, ballast) is applied to model the railway. A three-dimensional geometry is studied in this paper: it is a layered solid on a half space subjected to a vertical harmonic rectangular load moving with a constant speed. Results are shown for one porous layer on a half-space medium coupled to the beam. Numerical results are presented in both the spatial and the wavenumber domains for sub- and super- Rayleigh regimes. Results deal with the solid vertical displacements on the surface of the soil medium. The analysis shows that displacements are 3 times lower when the track is implemented on the ground. However, the soil dynamic response is reduced for this configuration in both the static and the dynamic cases and displacements appear in both x and y directions. Otherwise, the amplitude of displacements is more important when the load speed increases for the two configurations. Furthermore, results show the existence of a critical layer and a critical thickness for a non-moving load and its evolution when this latter moves. Thus, the influence of the critical thickness is significantly attenuated or canceled by speed load. For a small thickness, there is no wave propagation for a non-moving load and a sub-Rayleigh regime. Otherwise, waves occur when regime becomes super-Rayleigh. The passage of the sub-Rayleigh to super-Rayleigh one does not present important changes except larger field displacements behind the load, for higher speeds.