Experiments on dispersion-reinforced polymers have shown that friction at the matrix-filler interface contributes significantly to resistance to deformation. Cyclic-loading experiments on specimens after adhesive debonding at various external pressures indicated enlargement of the hysteresis loop with increasing pressure and percentage filling, an effect explained by the attendant enlargement of the friction surface. The contribution of interphase friction to the deformation processes is confirmed by experiments on physical models in the form of an elastic matrix in contact with the friction surface. With construction of a mathematical model in mind, experiments were performed to determine the law of friction of a polymer against a rigid surface. The resulting formula incorporates an essentially nonlinear dependence of friction force on pressure and slip speed. The results of the experiments were used in mathematical modeling of the deformation processes of a polymer in the presence of friction. Stretching and cyclic-loading regimes were studied in an elastic strip in constant contact with a friction surface as determined from an empirical relationship derived earlier. Loading of the strip was calculated step by step, with successive inclusion of the partitioning elements of the strip into the deformation process.