The work considers mathematical modeling deformation mode of elastic-plastic material in the ring and in the convergent radial channel with the assumption of asymmetrical propagation of shear localization lines in the shape of the logarithmic spirals. The equations of the state in the shear localization zone are used instead of conditions in the curvilinear cuts that represent functional relationships between normal and tangential components of vectors of stress increments and displacement increments. The displacement fields and stress fields are constructed.

Key words: shear rupture, shear localization, elastic-plastic material, finite element analysis.