Reasonable approximations and simplifications of the coupled wave equations of stimulated Brillouin scattering (SBS) in fibers are carried out. Based on the coupled wave equations of transient SBS, a numerical model is built. As these coupled wave equations of SBS are solved, especially in the tapered fiber with variable core diameter, the powers of the pump wave and the Stokes wave in the process of SBS are obtained, including the variation laws of them and the distinctions of the SBS in the fibers with different parameters. Based on the analyses, the parameters of the tapered fiber, which is used as a phase-conjugating mirror in high power and high repetition rate laser diode pumped solid state lasers, are optimized. It provides parameter optimization rules of the system in the applications for beam quality improvement. In addition, the rationality of the model is verified by comparing simulation results with experimental results.