Abstract: Combining the unified strength theory with a physical model of rock which describes the relationship between dynamic strength and strain rate effect, a unified rate-dependent dynamic strength criterion of rock was established under dynamic loading. According to the revised soil disc model, computing formulae of whole average floating lock stress and strain were deduced with the consideration of strain rate effect, intermediate principal stress effect, strength criteria and sliding friction of projectiles. On this basis, a calculating program was developed by the fourth order Runge-Kutta algorithm in MATLAB. Consequently, the penetration depth was gained in condition of medium-low speed (V ≤ 900 m/s) projectiles penetrating semi-infinite rock targets. Moreover, the motion law of projectiles and the dynamic response of targets were studied. The influential characteristics of some parameters on penetration depth were analyzed. The results indicate that the proposed computing method can precisely describe the dynamic responses of projectiles and targets during the whole penetration process. Through this method, a series of different criteria-based analytical solutions can be obtained and both the upper-and lower-bound limits of penetration depth can be predicted effectively. The intermediate principal stress effect, strength criteria and sliding friction of projectiles have important influence on the anti-penetration performance of rock targets.