Abstract: Considering the effect of shear strain of micro-void on damage evolution, a modified GTN model applicable to various stress triaxiality conditions is proposed by modifying the damage evolution mechanism of the GTN damage model. The modified model is implemented in commercial finite element software ABAQUS by combining the implicit stress update method with an explicit finite element solving algorithm and through the user-defined material subroutine VUMAT. The damage evolution and the failure process of pure shear and shear-tensile specimens are simulated by the modified GTN model, and the results show that the modified model is effective for various stress triaxiality conditions. Then, the modified model is used to simulate the crack initiation and the propagation of a steel strip with edge notch during a cold rolling process. The numerical result of the modified model is in a good agreement with rolling experimental observation, which indicates that the modified GTN model can reveal the complicated damage evolution behavior of a steel strip with edge defect in cold rolling. Numerical and experimental results show that the existence of edge notch in a steel strip can lead to cracks both in the front and rear of the notch, and the propagation of the rear one is more obvious.