This article is concerned with the parametric instability of circular plates elastically restrained against translation and rotation at concentric intermediate circles as well as along the periphery. The plate is subjected to a horizontal or tangential periodic radial load at the periphery. The instability regions of the plate both for the simple resonance and for the combination resonances of sum and difference types are determined analytically from the coupled Mathieu equations that are derived by applying the Galerkin method to the governing equations. The influences on the stability of the plate of the direction of periodic load and the stiffness of elastic supports are studied in detail for the plate with peripheral and one intermediate supports.