Various constitutive frameworks for macroscopic large strain elastoplasticity have recently identified the plastic spin as one of the key concepts in the description of anisotropic hardening. These theories involve a particular corotational stress rate that differs from the Jaumann stress rate by terms involving the plastic spin. This stress rate is introduced into a recently proposed material model for combined isotropic and kinematic hardening of a porous ductile solid. The plastic spin is taken to bc governed by the simplest possible constitutive law, involving only one additional material parameter. An analysis of so-called unconstrained shearing is used to illustrate the effect of plastic spin on the stress response at large strains and finite material rotations. The effect of the plastic spin, via the corotational stress rate, on the predictions of strain localization in shear bands is studied in terms of simple model analyses. Results for various deformation and void nucleation conditions are discussed. The plastic spin is found to have a significant influence on the onset of localization even though the material rotations are still rather small at that instant. Also the progressive evolution of the shear band after localization until ductile fracture occurs in a void-sheet is strongly affected.