The relationship between polarization degree of the transmitted light and the parameters of the fiber sensing coil was deduced by using statistical average method based on the Jones matrix theory for the stimulated Brillouin scattering fiber optic gyros. The characteristics of the eigen state of polarization (ESOP) of the pump light and the stimulated Brillouin scattering light in the sensing coil were theoretically analyzed, and the conclusion about stability of the ESOP was obtained.