An analytical method of flexural vibration of a three-layered circular plate with a viscoelastic core is presented for non-axially symmetric modes, and damping properties are investigated numerically. For plates with elastic layers of equal Poisson's ratio, an eighth order system of equations of motion is derived, and it is shown that a solution can be obtained in terms of Bessel functions. Axisymmetric modes are included as a special case in the present method. Numerical calculation can be carried out efficiently by use of the present method, so that this method is considered to be useful for the design of multi-layered structures. For axisymmetric and non-axially symmetric modes, frequencies and loss factors of plates with clamped edges and free edges are calculated numerically for a wide range of introduced parameters. The results are discussed and graphically presented