Theoretical model is established to study the Stimulated Brillouin Scattering (SBS) process with both noise initiation and seeding Stokes laser assisted initiation.Multi-steps finite difference method is adopted to solve coupled wave equations numerically, and the temporal and spatial profiles of scattered light intensity and density variations of the medium are obtained. The dependence of Stokes laser on SBS reflectivity and initiation thresholds is investigated.It is found that the time needed for SBS initiation decreases sharply since the seeding Stokes laser is introduced. Finally, the damage potential of the SBS process in optical materials is evaluated and future work is outlined.