In this paper, an elastic plastic damage model is presented based on the combined use of elastic plastic constitutive equations along with continuum damage mechanics. A tensile and a compressive damage variable are adopted to describe the different responses of concrete under tension and compression, respectively. The Helmholtz Free Energy is decomposed into hydrostatic stress component and deviatoric stress components. The hydrostatic stress component is neglected and the deviatoric stress component is amended according to stress state, resulting in a more accurate description of the concrete’s response under multi-axial stress state. Finally, through several numerical simulations it is proved that the proposed model has the capability of simulating typical nonlinear performances of concrete material.