This paper deals with frequency analysis of a circular plate supported on a rigid concentric ring with translational restrained boundary. Natural frequencies of such a circular plate are computed for different sets of elastic translational restraints, and for various values of the radius of the internal ring support. Results for different modes of plate vibrations are computed and presented in a tabular form suitable for use in design. The effect of plate boundary conditions such as translational restraints and the radius of concentric ring support on natural frequencies of the circular plate are studied. Exact frequency values presented in this paper are expected to serve as benchmark solutions for assessing the accuracy of other numerical methods being used in the literature. © 2016, Polish Academy of Sciences. All rights reserved.