In the present report the flexural vibration damping of a three-layer composite plate is analyzed for several damping configurations. When homogeneous damping layers are applied on one or both sides of the plate, the damping mechanism is associated with the alternating extensional strain of the visco-elastic damping material. The damping achieved is roughly proportional to the product of the Youngs modulus and the square of the thickness of the damping layer. When a stiff layer foil covers the damping material, then the damping is associated with the shear motion of this material. The camping is proportional to the stiffness of the foil but, there is an optimum thickness of the damping layer, which is a function of frequency and temperature for each material. This optimum thickness may be quite small. The theoretical relations can be used to calculate optimum damping treatments for various applications. Experimental results are in gratifying agreement with the calculated values and verify the general validity of the various physical assumptions concerning the damping mechanism.