The formation and development of strain localization via shear banding is examined for an orthotropic material for the purpose of studying the effect of the plastic spin and the anisotropy upon the strain localization. First, the material instability analysis is carried out for an orthotropic elastoplastic material with plastic spin. By way of finite element analysis, full numerical solution is next obtained for plane strain block of an elastoviscoplastic material under tension or compression, and the shear band development is simulated. The results show that the plastic spin may hasten or delay the initiation of shear band development depending upon the deformation or loading type - compression or tension, the initial orientation of the orthotropic axes, and the algebraic sign of the plastic spin.