The article analyzes methods for solving problems on the drive systems' compacting effect on the support surface (soil). There are analyzed results of studies on the distribution of pressures and tensions in the contact surfaces depending on the propulsors' mechanical properties and the support surface's material. The article also includes an analysis of methods for formalizing contact surfaces and constructing mathematical models for determining the distribution of pressures, deformations, and tensions in the contact surfaces. Numerical methods for solving contact problems that have been used recently are not integral. To obtain such solutions, numerical FEM and DEM methods can be used for a specific problem, i.e. for a problem with a known geometric data source and specific mechanical properties of a contacting body. Based on the studies conducted, it was concluded that to understand the interaction of a deforming wheel with a deformable surface, it is necessary to use an analytical method for solving contact problems in a three-dimensional setting as the most general and productive. It’ll allow us to determine the geometrical dimensions and shapes of the contact spot, determine dependencies of the geometrical parameters of the wheel, rolling resistance, tension-strain state of the contacting surfaces depending on the loading conditions of the wheel, its mechanical properties, and the support surface.