The model of stimulated Brillouin scattering in fiber grating based Fabry-Perot resonator is studied. The analytical solution of steady state stimulated Brillouin scattering equations for the first-order Stokes wave is given, and its transmission power and reflection power are calculated. The analytical solution of pump wave at incident end and the equation of energy conservation with neglecting fiber attenuation are obtained. Numerical solution for second-order Stokes wave is then given using Shooting and Levenberg-Marguardt (L-M) methods under the boundary conditions. The dependence of the transmission power and reflection power of pump wave and Stokes wave on incident wave power is investigated. Furthermore, the distribution of the power of pump wave and Stokes wave in the Fabry-Perot resonator is simulated and discussed.