The propagation of waves in soil media is an important phenomenon in the field of dynamics of soils. Continuum models represent the soil deformation by field equations. In order to investigate the dynamic behavior of soil media, one-dimensional wave propagation is a common benchmark case, which has been analytically solved by other authors and is used as a verification example for linear material model of the proposed approach. In order to simulate the transmitting boundaries absorbing infinite elements are developed and implemented in the numerical analysis. The numerical modeling of the problem is performed by the general finite element software ANSYS, using the user programmable features (UPF) and developed modules for modeling of soil behavior. In order to reflect the propagation of waves numerical analysis is done by extensive parametric study using the infinite elements. The obtained results emphasise some key issues regarding the soil deformation during the wave propagation.