Raman intensity calculations have been performed for nine small main-group molecules using the Kohn-Sham density functional method. A combination of numerical and analytic derivation techniques was used as implemented in the program package DEMON. The effect of the applied functional, the basis set augmentation, and the numerical fitting of the exchange-correlation potential have been investigated along with other aspects of the computations. The results obtained at the local level using valence triple-zeta plus 2 polarization functions (VTZP+) basis sets compare well with experiment and with the results obtained from the Hartree-Fock and correlation methods using large basis sets, whereas nonlocal corrections did not yield improvements in the predicted local Raman intensities. Systematic analysis proved the sensitivity of the results obtained with the gradient corrected nonlocal functional to the numerical fitting applied in the calculations of the exchange-correlation terms. We demonstrated that omitting the fitting procedure from nonlocal calculations improves the quality of the Raman intensities while the grid used for fitting does not have an influence on the Raman intensities; Effects of the reference geometry, step size for evaluating the numerical derivatives and the threshold of energy convergence were also tested.