Simulation of the contact interaction of the spherical bearing elements through an antifriction polymeric layer of three materials is considered in the work. The deformation theory of elastoplasticity was chosen as a model describing the behavior of antifriction polymers based on the results of experiments. In the framework of the numerical study it was found that the deformation path in the space of the principal values of the strain deviator have a low degree of curvature at the contact deformation of the bearing, which confirms the choice of the theory of small elastoplastic strains. The relative analysis of the deformation behavior of antifriction polymeric materials as an interlayer of a spherical bearing is carried out in the work. It was found that the antifriction layer of the modified PTFE provides a more favorable distribution of contact parameters: disconnection of contact surfaces near the free edge of the interlayer is absent; the decrease in the efficiency of the part of the structure is observed by 10% of the contact surface; the distribution of contact pressure and contact tangential stress is more uniform and minimal in magnitude than in the other two materials under consideration.