Mechanical characteristics of soil under static and dynamic strains are determined experimentally. Their accuracy and reliability depends on quasi-static nature of strain process in soil. The independence of experimental results on the wave processes is ensured. Laboratory devices of dynamic loading (DDL) have been used to determine the laws of dynamic strain and mechanical characteristics of soil. The quasi-static nature of strain process in soil on DDL is achieved solving the wave problem corresponding to experiment. Plane wave propagation in soil is considered; its statement is adequate to experiment on DDL. To describe the dynamic strain of soil, the G.M. Lyakhov elastic-viscoplastic model has been adopted. The system of differential equations in partial derivatives of hyperbolic type, describing the wave process, has been solved by the method of characteristics and finite difference method in an implicit scheme. The changes in wave parameters over time for different sections of soil layer have been obtained by numerical solution. The effect of layer thickness on wave parameters and on quasi-static process is shown by experiments. Quantitative and qualitative influence of mechanical characteristics of soil on wave parameters is determined. Analyzing results, it has been established that the main factors determining the quasi-static process are the parameters of dynamic load and the thickness of soil layer in DDL. The dependence of mechanical characteristics of soil on quasistatic nature of dynamic strain in DDL is shown. Conditions to ensure the quasi-static process of strain in soil sample under dynamic compression on DDL are obtained.