It is known that damage or inelastic softening can cause an ill-posed problem leading to localization and mesh-dependence in finite element simulations. In this paper, a nonlocal hardening variable, ̄𝜅 , is introduced in a finite deformation Eulerian formulation of inelasticity with a rate-independent smooth elastic–inelastic transition. This nonlocal variable is defined over an Eulerian region of nonlocality, which is a sphere with radius equal to the characteristic length, 𝐿c, defined in the current deformed geometry of the material. Two models of this nonlocal hardening variable are explored. One model where ̄ 𝜅 is the minimum value of the local hardening 𝜅 within the region of nonlocality, and another model where  ̄𝜅 is the average of 𝜅 in the same region. The influence of the nonlocal hardening variable is studied using an example of a plate that is loaded by a prescribed boundary displacement causing formation of a shear band. Predictions of the applied load vs. displacement curves and contour plots of the total distortional deformation of the plate and the hardening variable 𝜅 are studied. The model based on the minimum value of 𝜅 in the nonlocal region predicts mesh-independent post-peak response of the load vs. displacement curve. Also, it is shown that the characteristic material length, 𝐿c, controls the structure of the shear band developed in the plate.