The plates under study are treated with an unconstrained damping layer which is applied either partially or throughout the plates. Several configurations of partial damping layer treatment has been studied and in all the cases the volume of the damping material has been kept the same. When such a plate is subjected to a harmonic excitation at one of the resonating frequencies the magnitude of the amplitude of vibration and the dynamic stresses developed in the plate will depend mainly on the damping ratio. The stresses in the damping layer depend on the damping ratio and at the same time also on the thickness of the layer. Three boundary conditions are considered and the force of excitation is of a point harmonic type. The analysis is carried out for first two modes of vibration. © 1993.