Aiming to establish the estimation method of gear noises, the authors derived the basic theory for estimation of radiated sound power from the definition of the loss factor given by Ungar and Kerwin, without using the statistical energy analysis method. The theory was applied to the circular plates with a solid shaft as a simple model of gear bodies, and the vibration modes of the plates were analyzed under the assumption of mode damping. By using the result of the modal analysis, the equations for calculating the frequency spectrum of the three important parameters for estimation, the total loss factor, the driving point mobility and the radiation loss factor of the plates, were theoretically derived.