Abstract The research includes the development and analysis of a mathematical model of a truly viscous lubricant in a modified sliding bearing design with a composite fluoroplastic coating on the surface of the shaft and a groove, which helps to improve the distribution of lubricant and increase the durability of the system. Based on the equation of motion, the liquid lubricant under study, the continuity equation, and the equation of state, new mathematical models have been obtained that additionally take into account a parameter such as compressibility. The novelty of the work lies in the development of a methodology for engineering calculations of the design of a radial sliding bearing with a polymer coating, taking into account the presence of a groove, as well as the dependence of viscosity on pressure and compressibility of the lubricant, allowing one to determine the value of the main tribotechnical parameters. The results of the study provided a reduction in errors in bearing capacity by 11–13%, and in coefficient of friction by 9–12% of the modified bearing in comparison with traditional designs. As a result, it was possible to achieve an increase in the service life of radial bearings, which is of great importance for their industrial application.