In this paper, we numerically study the influence of material and laser parameters on laser spatial beam uniformity improvement based on stimulated Brillouin scattering (SBS). Owing to the intensity dependent property of SBS, the higher intensity parts of the laser beam experience a deep reflection, while the other parts transmit through the medium with weak reflection. Then, the uniformity of the input laser beam is improved. A single frequency laser with a 20th order super-Gaussian shaped output pulse was used as the pump. Five typical liquid materials were adopted as the Brillouin medium for comparison. The laser wavelength was set to 527 nm and 1053 nm; and the pulse duration was set to 3 ns and 5 ns, respectively. The numerically calculated results indicate that low gain coefficient and short phonon lifetime mediums (such as FC-70) are more suitable for the above-mentioned laser beam smoothing scheme. Meanwhile, short wavelength and pulse duration would be helpful for laser beam uniformity improvement. The energy efficiency is above 90% when the laser beam uniformity is greatly improved with an optimized input laser intensity. The calculated results are quite useful for high-power laser applications.