In order to study the cumulative damage characteristics and laws of rock masses under cyclic blasting loads, based on the finite element software ANSYS/LS-dyna and the HJC constitutive model, a single blasting damage analysis is conducted first, and the accuracy of the results is verified. On this basis, numerical simulation studies on the cumulative damage of rock masses under cyclic blasting are carried out separately. The results indicate that the cumulative damage evolution cloud map of the rock mass under cyclic blasting is similar to that of a single blasting action, showing an inverse S-shape overall. The damage increment of the rock mass decreases with the increase of blasting times, and in the central area of the damage zone, the rock mass is particularly affected by the superimposed effect of cyclic blasting loads. Cyclic blasting fully reflects the accumulation of damage to the rock mass under multiple cyclic blasting loads, and there is a certain relationship between rock mass damage and the distance between the blasting centers. As the distance between the blasting centers increases, the amount and increment of rock mass damage generated by blasting continue to decrease.