The bending wave is important at lower frequencies for the radiation of sound into water or air by a vibrating ship hull or large structures. It is for this reason that the reduction of radiated sound can be accomplished through the reduction of energy carried by the bending waves. Hence, applying damping by means of viscoelastic layers on the plates is one method of reducing bending wave energy in structures. However, the relationship between the radiation efficiency of noise and the viscoelasticity of plates has not been well investigated. In this paper, we attempt to clarify the relationship theoretically, and experimental results are also described.