Abstract: In order to improve the capability of Chaboche’s unified visco-plastic model in describing the tertiary creep,with Kachanov’s equation of damage evolution based on Lemaitre’s effective stress being used,Chaboche’s visco-plastic potential function was utilized to obtain the inelastic flow rule and hardening rule coupling to damage.It is shown that the form of the evolutionary equations of internal variables remains the same, and that the damage variable is not explicit in the equations.The modified constitutive model with damage was applied to the description of the uni-axial and bi-axial creep behaviors of a Ni-based superalloy,Udimet 720 Li,by coding the user’s material subroutine,UMAT,in ABAQUS platform.The finite element analysis of cruciform specimens shows that the inconsistency between uni-axial and bi-axial creep modeling capability exists in Kachanov’s damage law,especially at the time of rupture.The calculated creep behaviors match well with the experimental ones when a multi-axial damage factor is introduced into the damage evolutionary equation.