In this paper a methodology for the computation of Raman scattering cross-sections and depolarization ratios within the Placzek Polarizability Theory is described. The polarizability gradients are derived from the values of the dynamic polarizabilities computed at the excitation frequencies using ab initio Linear Response Theory. A sample application of the computational program, at the HF, MP2 and CCSD levels of theory, is presented for H2O and NH3. The results show that high correlated levels of theory are needed to achieve good agreement with experimental data.507511Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)