By adopting noise initiation model of stimulated Brillouin scattering (SBS), the influence of phonon lifetime and gain coefficient of medium on power limiting characteristic is numerically investigated. Through using actual parameters of three media, CCl4, acetone, and CS2, the waveforms of transmitted pulses are simulated. The result shows that different media have little effect on the front peak of waveform, while have an obvious effect on the height of power limiting platform. When the medium which has short phonon lifetime and small gain coefficient is used, the height of power limiting platform is comparatively high. In experiment, by focusing 1064-nm, 8-ns, 18-mJ pulses into these three media, the waveforms of transmitted pulses are obtained. The experimental results are in good agreement with conclusions of theoretical simulations.