This study is devoted to the development of a new mathematical model, a wedge-shaped sliding support with a non-standard elastically deformed support profile of the slider surface, taking into account nonlinear factors, under conditions of a two-layer lubricant flow, providing effective lubrication and reducing wear of the working surface. To develop this model, we will use mathematical modeling and data analysis methods to take into account all the necessary factors and parameters. To achieve this goal, well-known nonlinear equations are used: the motion of a viscous incompressible fluid for a "thin layer", the continuity equation and the Lame equation with appropriate boundary conditions, taking into account the elasticity and adaptability of the support surface of the slider, as well as equality of velocities at the interface of stratified layers, equality of pressure at the ends of the interval and equality of velocities on the surface of the guide. As a result, the main performance characteristics of the ras were identified

Keywords: nonlinear factors, elastically deformed, non-standard surface, flow of two-layer lubricant, dependence of viscosity characteristics of lubricating layers, ratio of density characteristics