Parameters including pump energy, beam waist radius, length of gain medium and beam divergence all affect the generation threshold and output pulse characteristics of lasers that utilize the stimulated Brillouin scattering (SBS) effect. In this paper, we investigate the effect that changes to the pump beam focusing parameters (namely beam divergence and beam waist) have on the output characteristics of the Stokes beam generated through the SBS process. This study is conducted both theoretically and experimentally using a single-cell SBS structure. The results highlight that pump beams with a small divergence angle at the focal point within the SBS cell are favorable for the generation of Stokes beams with short pulse lengths. Here, we demonstrate the generation of a Stokes beam with a pulse width of 854 ps using a pump pulse with a pulse width of 7.2 ns, which was focused to a spot with a divergence angle of 2.48 mrad.