Abstract: The accurate description of mechanical characters of the mass concrete structure under multi-axial loads is essential to the reasonability of structure design. In this paper, a constitutive model is established which combines the damage mechanics and failure criteria. It improves the existing failure criteria which do not take into account the effect of micro damage in material. The developed program is employed to compute the whole process of arch dam from damage to crack to failure, using 3-D nonlinear FEM analysis. In comparison with that obtained by other softwares, the present computed results show that the proposed model is reasonable.