This research attempts to solve the problem of interaction between soil and structure at external dynamic impact. Here was included the properties of soil to absorb seismic waves. It is more comprehensive method and here was taken into account a viscous property of “soil-structure” interaction. This path is more advanced than the methods used in simplified ones. Statement of the problem can be applied in direct or variational form. In this issue, a system of integro-differential equations is compiled based on Ostrogradsky-Hamilton variational principles. For solving the problem, a numerical discrete model by using finite element method for hereditarily deformable systems was proposed. A method has been developed for calculating a viscoelastic infinite half-plane with taking into account a viscous fictive boundary for absorbing elastic waves. So technique by introducing fictive boundary is give us opportunity for obtaining more reliable solution for stress and strain state of structure. However, it should be noted that the rheological properties of the soil as the constitutive relations were not used in this article. The method is implemented by performing specific numerical calculations