Department of Mathematics, Altai State Technical University, Barnaul 656031, Russia ivan262@bk.ru Many fluid systems, including polymeric and bio-polymeric materials, reveal the anomaly of slipping often near the solid surface. The presence of such a wall effect leads to a violation of the hypothesis on attachment and the need to specify appropriate boundary conditions. This anomalous behavior of materials in a plastic state (slurry, grease, fluids and polymer melts) at solid surfaces requires a comprehensive study of both rheological properties and calculating the flow parameters and characteristics of the processing equipment. In the first place, there are rather complex problems of determining the rheological characteristics of the material results according to the viscometric studies. The next stage is associated with specific problems on the motion of fluids which exhibit abnormalities in solid surfaces and the direct use the sliding velocities as boundary conditions. This work is to specify explicitly the slip velocity at the wall, which is generally a function of stress at the wall, the geometric dimensions and temperature. And this dependence of slip velocity at the wall of these factors can be found from viscometric measurements. Next considering the case of plane Poiseuille flow with allowance for slippage of the polymer material at the boundary, the system of equations of the modified rheological model Vinogradov and Pokrovskii describes non parabolic velocity profile in the gap between parallel plates, which is confirmed by experimental data. The dependences obtained can be used in the study of more complex flows. This is shown by the example of the calculation of the three-dimensional velocity profile of a nonlinear viscoelastic fluid in a channel with a square cross-section. This work was supported by the Russian Foundation