Free axisymmetric vibrations of polar orthotropic annular plates of variable thickness resting on a Pasternak-type elastic foundation have been studied based on the classical plate theory. Hamilton’s energy principle has been used to derive the governing differential equation of motion. Frequency equations for an annular plate for two different combinations of edge conditions have been obtained employing Chebyshev collocation technique. Numerical results thus obtained have been presented in the form of tables and graphs. The effect of foundation parameter and thickness variation together with various plate parameters such as rigidity ratio, radius ratio, and taper parameter on natural frequencies has been investigated for the first three modes of vibration. Mode shapes for specified plates have been presented. A close agreement of results with those available in the literature shows the versatility of the present technique.