Stimulated Brillouin scattering (SBS) can be utilized in laser systems to improve alignment stability. The stability of SBS is a key factor of limiting the system stability. Combining with the theory of hydrodynamics, vibrating string and transient SBS, a new SBS model with longitudinal vibrating of media is established. The eigenvalue of vibrating is obtained by solving the model. Basing on the model, the influence of longitudinal eigenvibrating and harmonic vibrating of tetrachloride with different intensities on the Stokes beams is investigated theoretically. The result shows that the influence of vibration on SBS has a certain threshold. When the intensity of vibration is less than some value, the stability of SBS is not affected. Another numerical simulation is carried out to research the dependence of stability on the configuration of SBS. It shows that the stability is enhanced when choosing lenses with shorter focus and shorter media cell.