Highly filled trolymer comtrositions are widely used in various trrocesses of modern industry, and therefore the study of the flow of such non-Newtonian media in the various channels of trrocessing equitrment traid much attention. All the imtrortant factors that should be considered when develotring mathtdatical models of the flow of such media are covered. A model of the flow of strecial-filled rubber comtrounds in the channels with the energy dissitration, wall slitr, thermal boundary conditions of the third kind, and the detrendence of the viscosity on ttdtrerature and the degree of filler distrersion has been develotred.