Abstract: Under the impact load, sandstone usually fails when the damage quantity <i<D</i< is less than 1, and there exists the critical damage. Based on the fractal geometry theory and the structure features of sandstone, a 2×3 cellular model was established in this paper. The instability critical damage of sandstone is 0.4 after theoretical calculation, and the critical damage of stage change is 0.119. Results analysis of the <i<Φ</i<50 mm SHPB experiment shows that there are two critical points in the dynamic damage process of sandstone:the first critical point is from the linear damage stage to the accelerated damage stage, and the corresponded damage quantity is about 0.1; the second critical point is from the damage stage to the failure stage, and the corresponded damage quantity is about 0.4, which agrees well with the theoretical research. The study reveals the critical problem of sandstone failure in the damage process.