Highly filled polymer compositions are widely used in various processes of modern industry, and therefore the study of the flow of such media in the various channels of processing equipment paid much attention. Cover all the important factors that should be considered when developing mathematical models of the flow of such media. A model of the flow of special–filled rubber compounds in convergent channels with the energy dissipation, thermal effects on the compressibility of the mixture, the effect of wall slip, thermal boundary conditions of the third kind and the dependence of the viscosity and thermalphysic properties of temperature, pressure and the degree of vulcanization are considered.