The present article is devoted to the formulation of the problem and the development of a model for the vibration damping properties of the roadbed at the base of the ballast prism’s bottom of normalized thickness, a protective sand cushion and clayey soils under the influence of harmonic oscillations based on physical and chemical mechanics. When analyzing the interaction between the car and the railway, typically the Kelvin - Voigt body is used and the roadbed is represented as a certain adjusted concentrated mass participating in vibrations with sleepers and rails. But this model is inapplicable for layered systems that do not have, in principle, concentrated masses. Such problems can only be solved using the theory of wave processes. In addition, for the occurrence of oscillations in loam it is necessary to have a medium under it reflecting the vertical longitudinal wave. Otherwise, the reverse half-wave will not form, and the compression wave will go deeper and turn into heat in the end. Due to the reflection at the interface of the layered system in each layer, the amplitude and absorption of the energy of the harmonic oscillations will be different from the initial displacement amplitude of the rails. That is, such problems can be solved only using the theory of wave processes. In view of the reflection of deformation waves from the outer surfaces of the sleepers (faces, side surfaces) and their compensation, the task of modeling becomes a one-dimensional.