Axisymmetric vibrations of a polar orthotropic circular plate of variable thickness (linear as well as parabolic) resting on an elastic foundation of Winkler type are discussed on the basis of the classical theory of plates. An approximate solution of the problem is obtained by the Ritz method. Frequency parameters of plates with different edge conditions for the first three modes of vibration and for various values of the taper parameter, the foundation modulus and the rigidity ratio are presented.