In the paper, inelastic strain localization in homogeneous specimens and mesovolumes of a polycrystalline material is modeled based on the asymmetric theory of an elastoplastic Cosserat continuum in a two-dimensional formulation for plane strain. It is assumed that rotational deformation in loaded materials occurs due to the development of localized plastic deformation as well as bending and torsion of the material lattice at the micro- and nanoscale levels. For this reason, the parameters of the micropolar model are considered as functions of inelastic strain for each local mesovolume of the continuum. It is shown that the observed parabolic hardening can be attributed to a large extent to the development of rotational deformation modes, bending and torsion, and appearance of couple stresses in the loaded material. The modeling results indicate that if rotational deformation is stopped in the loaded material, its accommodation capacity decreases, the local and macroscopic inelastic strains sharply increase, leading to a much more rapid formation of fracture structures. Conversely, the formation of meso- and nanoscale substructures with high lattice curvature in materials promotes the activation of rotational deformation modes, reduction of localized strains, and relaxation of stress concentrators.