In this study, based on the wave equation and material equation of a solid Raman medium and neglecting the transient effect of stimulated Raman scattering, the coupled wave equations of the interaction of the first anti-Stokes beams, the pump, and first to third Stokes beams in extra-cavity pumped anti-Stokes lasers are obtained using the plane wave approximation. Normalized parameters are introduced to normalize the equations. The effects of the normalized Raman gain coefficient, normalized pump pulse width, and normalized wave mismatch on the performances of extra-cavity pumped anti-Stokes lasers are analyzed by numerically solving the normalized coupled wave equations. The experimental data are substituted into the coupled wave equations. The theoretical estimations of the anti-Stokes optical conversion efficiencies are consistent with the reported data, which validate the correctness of the theoretical model. By analyzing the theoretical calculation results, methods to improve the conversion efficiency of extra-cavity pumped anti-Stokes lasers and associated methods of lasers design are proposed.