The aim of this paper is to develop an analytical-three-dimensional model for stimulated Brillouin scattering (SBS). The transversal effects on SBS are analyzed with Gauss-Laguerre orthonormale polynomial development. The correlation integrals which contain the information of transversal effects on SBS are described. Using the development of orthonormale polynomial in transversal plan, as solutions of wave equation we identify (have found) solutions of "discrete spectrum" (development on Bessel function) and solutions of "continuum spectrum" (solve of integral equation for Gauss-Laguerre polynomials). We have determined the total SBS reflectivity for (0, 0) and (0, 1) modes and is show how the transversal effects affects the SBS reflectivity. In this sense, we have calculated the Gaussian beam dependence function by Brillouin gain. The results are similar to the experimental result for both (0, 0), (0, 1) modes.