The paper proposes a new numerical method to predict the growth behavior of the multiple PWSCCs in the primary alloy 600 components. The method based on the PWSCC initiation model and macroscopic phenomenological damage mechanics approach can induce same results irrespective of the element size. The assessment method was verified comparing with the previous study results. The verified method was applied to collinear and parallel axial surface cracks. As a result, for the collinear crack, the penetration times of the collinear cracks are earlier than those of the single cracks, and the penetration time increases with increasing the space between two cracks. For the parallel crack, the penetration times of the parallel cracks are later than those of the single cracks, and the penetration time increases with decreasing the space between two cracks.