Highly filled polymer compositions are widely used in various processes of modern industry, and therefore the study of the flow of such non-Newtonian media in the various channels of processing equipment paid much attention. All the important factors that should be considered when developing mathematical models of the flow of such media are covered. A model of the flow of special-filled rubber compounds in the channels with the energy dissipation, wall slip, thermal boundary conditions of the third kind, and the dependence of the viscosity on temperature and the degree of filler dispersion has been developed.