axially symmetric plastic deformation, an ideal current, a thick-walled pipe, the smooth curvilinear tool, hardening. 

The axially symmetric processes of plastic deformation of thick-walled pipes by the smooth curvilinear tool on external or internal borders are considered. The ideal plastic current of the stiff-plastic body is accepted at coincidence of the main pressure to the current lines. It is defined the free internal or external border of plastic area from which the current lines, the fields of pressure and speeds are calculated by a numerical method and the tool profile is set. The condition of plasticity of Mises is used taking hardening into account