Nonlinear dynamic analysis of circular plates on two parameter elastic foundations is studied. Winkler and Pasternak models of elastic foundation are used. The nonlinear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the discrete singular convolution (DSC) in the space domain and the harmonic differential quadrature (HDQ) method in the time domain. The influence of stiffness of Winkler (K) and Pasternak (G) foundation on geometrically nonlinear dynamic response of plates is investigated. The influence of damping on the nonlinear dynamic response has also been studied. Numerical results obtained by the application of present technique compare well with the results available in literature.