Abstract: On the basis of the theory of thin plate of small deflection and the constitutive equation of KelvinVoigt, the governing equation of the viscoelastic annular plate is established. The natural frequencies and modes are calculated, respectively, in consideration of the boundary of the clamped inner edge and the free outer edge by employing the method of separation of variables. The results are compared with those obtained by the finite element method. The effects of the core ratio and the inner-outer radius ratio on the natural frequencies and the damping coefficient are discussed. Conclusions are as follows: the natural frequencies increase at first, then decrease with the increase of the core ratio,however,the damping coefficient increases with the increase of the core ratio. The natural frequencies and the damping coefficient also increase with the increase of the inner-outer radius ratio.