Solution of the problems of longitudinal interaction of underground pipelines with soil in a one-dimensional statement requires precise measurements of the thickness of the soil layer contacting with the pipeline. In order to determine the dimensions of the contact layer of soil, the behavior of soil medium under shear interaction of a rigid body with soil is studied. Under straining in soil medium, structural changes denoted by the coefficient of structural destruction are taken into account; the condition of complete adhesion is taken in the contact rigid body – soil boundary. The interaction process under consideration is investigated numerically by the finite difference method. The results of the calculations are presented in the form of graphs and are analyzed. From the obtained results, the maximum values of the thickness of soil contact layer are determined as well as the layers with the corresponding degree of structural destruction depending on the geometric dimensions of the rigid body.