Stimulated Mandelstam-Brillouin backscattering of light is analyzed with the aid of the inverse scattering problem method. An asymptotic solution of this problem is obtained, as well as a solution for weak fields. It is shown that, just in the case of forward stimulated Mandelshtam-Brillouin scattering, the effective-interaction region, in which the intensity of the incident light wave is transferred to the scattered one, shifts towards the entrance face of the sample. It is also established that the asymptotic rate of decrease of the acoustic and scattered waves is independent of the rate of decrease of the initial distribution. The parameters characterizing the initial conditions are contained only in the pre-exponential terms.