Abstract: The coupled wave theory of nonlinear optics and continuous equations of hydromechanics are adopted to establish two-dimensional theoretical model of seeded and narrowband pumped transverse SBS. Based on these equations, investigations of the effect of broadband pump on Stokes gain are presented by numerical simulations. The investigation shows that the SBS gain will decrease significantly if laser bandwidth are a little greater than the SBS linewidth. Greater the bandwidth, less the Stokes gain. The bad effects induced by transverse SBS can be suppressed when the bandwidth is greater than 20GHz. On the other hand, modulation frequency will influence Stokes gain and the optimal frequency through the numerical simulations can be chosen.