The formation of strain localization in the form of shear banding is examined for an orthotropic elasto-plastic material for the purpose of studying the effect of the plastic spin and the anisotropy upon the strain Localization. The material instability analysis is carried out for an orthotropic elasto-plastic material with plastic spin in the state of plane stress. 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.