This paper deals with the study of the vibration characteristics of thin circular plates with elastic edge support and resting on an elastic foundation. The Winkler model describes the foundation. The exact analytical method is used to derive the frequency equation of the plate with elastic edge support and resting on an elastic foundation. The basic equations are those which are obtained from classical thin plate theory. Parametric investigations on the vibrations of circular plates with elastic edge support and resting on an elastic foundation have been carried out with respect to various values of translational stiffness ratio, rotational stiffness ratio, foundation stiffness ratio and boundary conditions. The results for 12 modes of vibration are presented for each case considered, and extensive data are tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint, rotational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates. © 2012 King Fahd University of Petroleum and Minerals.