Abstract: Based on the unified strength theory, considering the effect of intermediate principal stress and lateral free boundary of target to analyze the elastic-plastic stage and plastic stage of the linear strain-hardening target material, analytical solutions of radial pressure on the cavity wall are obtained and the unified penetration model of the linear strain-hardening target material is built. On this basis, resistance formulas and penetration depth formulas of the rigid projectiles with medium-low speed (v₀≤1000 m/s) penetrating into metallic thick target finite in radial extent are deduced, then their solutions are obtained by utilizing the Simpson method. Meanwhile, influencing factors for ballistic terminal effects including strength criterion difference are 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 are obtained and the ranges of penetration depth of targets under different striking velocities are predicted effectively. Moreover, various parameters have influences on the anti-penetration performance of the target, such as the strength parameter, the striking velocity, the target radius and the shape of the projectile nose; among them the penetration depth has increased by 22.45% as the strength parameter value changes from 1 to 0. In addition, as the ratio of target radius to projectile becomes smaller, the penetration depth becomes bigger, and it has increased significantly when this ratio is less than or equal to 16. It is indicated that the penetration depth is obviously affected by the target boundary size at this time, and it cannot be calculated as an unlimited-size target any more.