The cyclic blasting in tunnel excavation inevitably causes cumulative damage to the surrounding rock. In view of the deficiency that the explosive load is almost simplified as an impact load in the current numerical simulation studies, the Bandaki micro-blasting test was first numerically reproduced based on the LS-DYNA software, which verified the rationality of the RHT constitutive model, ALE coupling algorithm and material parameters adopted in the numerical model. Secondly, the real explosion process of 88 blast holes in a certain tunnel section was truly simulated by this software, which overcame the shortcomings of the current methods that failed to consider the effect of blast gas and simplification errors, and improved the calculation accuracy. At the same time, the complete restart technology and the initial in-situ stress application method were adopted to well simulate the cumulative damage mechanism of the surrounding rock of the tunnel under the coupling effect of cyclic blasting and initial in-situ stress. Finally, based on the above numerical model, the cumulative damage mechanism of the surrounding rock of the tunnel under different in-situ stress conditions caused by cyclic blasting was studied. It was found that with the increase of the number of cyclic blasting, the damage range of the surrounding rock gradually expanded, and the cumulative damage effect was obvious. The initial in-situ stress had a significant inhibitory effect on the damage of the surrounding rock of the tunnel, and the damage range decreased with the increase of in-situ stress. Taking the third cyclic blasting as an example, when the initial in-situ stress gradually increased from 0 MPa to 10 MPa, 20 MPa and 30 MPa, the average damage range of the surrounding rock gradually decreased from 64.05 cm to 20.99 cm, 13.34 cm and 7.01 cm, with the reduction rates of 67.2%, 36.4% and 47.45% respectively, that is, the reduction rate generally showed a gradually slowing trend. The research results can provide useful references for tunnel blasting excavation engineering.