In the paper a model of a local contact of a polymer-based nanocomposite was developed within the method of a movable cellular automaton. The features of mechanical behavior of nanocomposite at the mesoscale level under dry sliding were studied with explicit account for the microprofile of the counterbody surface and the characteristic sizes of nanofiller. Factors that contribute to the conditions for the formation of a stable tribofilm of silica nanoparticles are analyzed. Two other parameters like sample geometry and the value of relative sliding velocity are also examined. It is shown that the thickness of tribofilm depends on stress conditions at the contact, and the friction coefficient decreases with increasing sliding velocity similar to one observed experimentally. To ensure the low friction properties of polymer nanocomposite, particles whose sizes are comparable with the characteristic size of the substrate microprofile are preferred. Results of numerical simulation are in good correlation with available experimental data.