In this paper, a new formulation is presented for the analysis of circular plates supported on elastic foundations. The formulation is based on the flexibility and stiffness methods of structural analysis. Classical thin plate theory for small deformations is applied to obtain the flexibility and stiffness coefficients. The circular plate is represented as a series of simply supported annular plates resting on support springs along their common edges. The computer implementation of the method is given, and solutions obtained for an illustrative case are discussed.