Brillouin scattering of light from certain crystal plane of polished single crystal spheres was measured. From the obtained data of sound velocity anisotropy, all the elastic and piezoelectric parameters of the single crystals of Fe and Cr doped LiNbO3 were deduced. The results were compared with pure LiNbO3. Discussion indicated that the sign uncertainty of some elements of the elastic tensor was due to the choice of the coordinates.