Introduction. Properties of filled composites based on polytetrafluoroethylene allow them to work at high contact pressures, reciprocating nature of shear loads, and in a wide temperature range. Due to this, they are used as antifriction layers of bearing parts with ball segment. To simulate the mechanical behavior of such materials under operating conditions, adequate constitutive equations of elasto-viscoplasticity and methods of their identification according to the data of basic experiments are needed.Materials and Methods. The tensor-linear model of elasto-viscoplasticity should be identified according to the data of tests on free compression of samples. They were subjected to loading up to a maximum deformation of 10 %, allowed to remain, unloaded, and then, a similar loading cycle up to 160 MPa under constrained compression was carried out. The experiment with a composite based on polytetrafluoroethylene filled with 40 wt. % fine bronze, was conducted at room temperature. Tests for constrained compression were performed for two values of the strain rate, and for free compression – for three values of the strain rate in the range of 10-6 – 10-3 s-1. For the description, two models of elasto-viscoplasticity were considered, representing modifications of Swain and Kletschkowski’s models and corresponding to the connection of a viscoelastic or elastic nonlinear viscous element with a plastic or endochronic element. An integral operator with a Kohlrausch kernel was considered as a viscoelastic element.Results. The results of the constrained compression tests made it possible to separate the elastic relationship of volumetric deformations and average stresses from the constitutive relations. The data of free compression cycles at different strain rates were used to determine the material constants of the model. For this purpose, an efficient search algorithm based on the simplex method of minimizing the discrepancy was implemented. Both models discovered the importance of the plastic component (independent of the deformation rate) for a qualitative description of the stress cycling that accompanied the cyclic deformation, as well as their dependence on the strain rate.Discussion and Conclusions. Both models of elasto-viscoplasticity described correctly the behavior of the studied fluorocomposite under loading conditions close to the operating conditions of the antifriction layers of the bearing parts with ball segment. They can be considered as a basis for their further generalization, taking into account the dependence on temperature.