Abstract: To know the objectivity of non-local damage models when the strain-softening phenomenon is simulated, several non-local damage models are introduced in this paper. Next, a simple tension bar is studied with analytic method to see if these models can overcome the two problems associated with strain softening zero consumption of energy and mesh dependence. The expressions of displacement about stress and mesh dimension are gained and displayed in diagrams. It is seen that some non-local damage models can overcome these two problems. Other models not only cannot solve these two problems, but also fail to reflect the actual response of structure. Thus, non-local damage models deserve further research effort.