Most studies of failure analysis in ductile metals have been based on the classical plasticity theory using the local constitutive relations. These frequently yields a physically unrealistic solution, in which a numerical prediction of the onset of a deformation localization shows an inherent mesh-size sensitivity. A one way to remedy the spurious mesh sensitivity resulted in the unreasonable results is to incorporate the non-local plasticity into the simulation model, which introduce an internal (material) length-scale parameter into the classical constitutive relations. In this paper, a non-local version of the modified Gurson constitutive relation has been introduced into the finite element formulation of the simulation for plane strain compression of the visco elastic-plastic void material. By introducing the non-local constitutive relations we could successfully removed the inherent mesh-size sensitivity for the prediction of the deformation localization. The effects of non-local constitutive relation are discussed in terms of the load-stroke curve and the strain distributions accross the shear band.