Based on the theory of continuous damage mechanics and the principle of irreversible thermodynamics, the damage evolution model of low cycle fatigue is investigated. By programming the damage evolution model as UMAT subroutine in ABAQUS, the fatigue damage and crack initiation life of notch materials under specific loads are simulated, and the crack initiation location is determined. Furthermore, the effects of root radius, depth and opening angle on crack initiation life are investigated. The results show that the crack initiation occurs easily in the notch root where the damage is the most serious and the plastic strain accumulates fastest under cyclic loading. With the increase of notch depth and root radius, the crack initiation life decreases. For V-notched specimens, when the notch depth remains unchanged, the crack initiation life will decrease with the increase of the opening angle.