We present Stimulated Brillouin Scattering (SBS) process in AlGaN integrated photonic waveguides. The wide bandgap of this III-Nitride material platform allows operating at visible wavelengths enabling large Stokes shifts. For this study, we employ a multiphysics approach that includes electric-photoelastic, magnetic-photoelastic, material interface displacement effects, and for optimal waveguide dimensions to find the Brillouin-active acoustic modes involved in the SBS process. The SBS power gain and the Stokes frequency shift are investigated for both backward and forward scattering processes, and it is shown that stokes shift larger than 50 GHz with high gain are achievable. Moreover, a parametric analysis is presented in order to demonstrate the possibility of realizing Brillouin lasers operating at blue wavelengths.