A quasi-static finite cavity cylindrical expansion model is proposed to investigate the lateral boundary effect during long-rod penetration. Analytical solutions for the cavity pressure in the elastic–plastic stage and plastic stage are obtained, through which a decay function for the lateral boundary effect is constructed. The resistance of the target with finite diameter R_T is obtained by multiplying the decay function with the resistance of infinite target R_T*. Then, a theoretical model for the penetration into the metal targets with finite diameters by long rods is proposed by substituting R_T into the Alekseevskii–Tate model. The proposed model is verified by comparison with existing experimental results. Furthermore, the effect of the target diameter, initial impact velocity and yield criterion on the penetration depth and resistance are investigated. The results showed that the lateral boundary effect should be taken into account if the ratio of the target radius to the rod radius (r_t0/R_P) is less than 25.