In this work, numerical methods to identify the surface areas of a vibrating structure that radiate sound are implemented for cases of structures with inhomogeneous distributions of viscous Rayleigh damping. The intensity-based techniques correspond to acoustic intensity evaluated in terms of the acoustic pressure and particle velocity, non-negative intensity evaluated in terms of the acoustic impedance matrix obtained at the structural surface, and back-calculated non-negative intensity evaluated in terms of the acoustic impedance matrix obtained at a far-field receiver surface. Different configurations of inhomogeneous damping are applied to two elastic structures corresponding to a plate and a cylindrical shell. To examine the influence of inhomogeneous damping on sound radiation, the acoustic intensity on the structural surface, the acoustic intensity on several different far-field receiver surfaces, non-negative intensity and back-calculated non-negative intensity are numerically compared for different inhomogeneous damping cases.