Failure of sheet metals by localized necking under biaxial plane stress loading conditions is simulated using a multi-surface porous plasticity model that accounts for plastic orthotropy of the material. The effective yield surface is determined as the inner envelope of individual yield surfaces corresponding to diffuse yielding of a micro-scale porous representative volume element, referred to as homogeneous yielding, and localized yielding of the inter-void ligaments along a band of voids, referred to as inhomogeneous yielding. The macroscopic yield locus predicted by the model at finite porosities has a piece-wise smooth appearance, consisting of alternating curved and flat segments corresponding to homogeneous and inhomogeneous yielding, respectively, at the micro-scale. The predicted yield loci are validated by comparison with quasi-exact yield loci obtained using finite element simulations of micro-scale porous unit cells subjected to proportional loading. A plasticity-model based on the above yield criterion is integrated under proportional plane stress loading paths, and predictions for the onset of localized necking in thin sheets are obtained using the plastic instability criterion of St¨oren and Rice [1]. The normality flow rule is used to determine the plastic flow direction for the smooth parts of the yield surface, while the flow direction at the yield vertices is determined using the assumption of fully active loading and the resulting consistency conditions. It is shown that the presence of vertices on the yield surface leads to realistic predictions of the necking limit strains for both negative and positive values of the minor strain using the plastic instability criterion; unlike the case of smooth plasticity models that predict infinite ductility for positive minor strains. The predicted shapes of the forming limit curves are in qualitative agreement with experiments, and accounts for the effects of strain hardening and plastic anisotropy parameters on the necking limit strains.