Using, as an example, a crack of normal separation in a steel of the austenite class, the evolution of a plasticity condition, which is attributed to the strain hardening of the material, as well as its influence on the length of a plastic zone near the crack tip on crack's continuation, are studied. As a result of the strain hardening that is realized in accordance with the isotropic-kinematic-type hypothesis, the material has transformed into a transversely isotropic one. Two variants of the crack orientation with respect to the symmetry axis of the material and in the perpendicular direction are considered. It is shown that, during a plastic deformation, the relation linking isotropic and kinematic components of the hardening does not remain constant and changes in the direction of an increase in the portion of the isotropic component. In the area, where the kinematic component dominates, the length of the plastic zone in both cases of the crack orientation is maximal and depends slightly on the value of the plastic strain. In passing to the area where the isotropic component is dominant, the plastic zone length decreases with greater intensity in the case where the crack is oriented in the direction of the symmetry axis.