A Finite Element Method using a C++ code is developed to study the mechanical wave propagation in saturated porous soils. The modelization uses the complete Biot theory including the couplings between the solid and fluid phases. A matrix-free algorithm and a selection data technique are implemented in the code. Researches are focused on homogeneous and heterogeneous semi-infinite media in the case of transient regimes. The time domain results present the displacements over and within the half-space. In particular, we will see that the fluid wave front is strongly dependent on the proportion of heterogeneities in the ground.