plasticity, technological problems, the field of rates of displacements, the upper estimate of deformation efforts.

The question of construction of continuous fields of rates of displacements at plastic flow of material with a smooth profile is considered. Differential equations and the first definite integrals are obtained. Using the boundary conditions on the input material in plastic region the Cauchy problem is solved and rates of displacements are determined. As an example, the velocities field for the matrix, the profile of which is limited by circular arcs, is defined. A comparison of the efforts the deformation with the exact solutions for the flow of material through the sigmoid matrices is conducted.

Korobkin Valery Dmitrievich e-mail: v.d.korobkin@yandex.ru, Doctor Sci. Phys. & Math, Professor, Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia. Ordyan Mikayel Gareginovich e-mail: omg84@mail.ru, PhD in Phys. & Math, Assoc. Professor, Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia.