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This paper treats the Brillouin backscattering in a single mode optical fiber and its implications on the Brillouin Ring Laser Gyroscope (BRLG). The BRLG consists of a fiber ring cavity in which stimulated Brillouin scattering is induced and provides two resonant counterpropagating backscattered waves. If this cavity is rotating around its axis, the backscattered waves get different resonant frequencies because of the Sagnac effect. The frequency difference is proportional to the rotation rate (Omega) by inducing a frequency offset between the counterpropagating waves. Some reported Brillouin spectra exhibit several peaks, which means that one pump wave provides at least two backscattered waves with distinguishable frequencies. In order to understand this multi-backscattering and to take advantage of it for the BRLG, we present results of a simulation of the Brillouin backscattering in a single mode optical fiber.