Abstract The general development of the theory given here considers the material to be orthotropic and continuous over ( n−1) elastic or rigid supports. The effect of rotatory inertia and in-plane loads are also included while formulating the equations of motion. Double and triple series solutions are given for orthotropic continuous plates. By matching the continuity conditions at the intermediate supports and satisfying the boundary conditions at the outer edge, the frequency determinant is obtained. For the purpose of numerical computations, an isotropic plate continuous over an intermediate-rigid or elastic-support and free and with no in-plane loads at the outer edge is considered. It is found that the influence of Poisson's ratio on the frequency parameter is significant only for the first symmetric or asymmetric modes. The rotatory inertia influences the frequency parameter when the radius to thickness ratio is less than 80, viz, when the plate is thick. Moreover, the elasticity of the support influences considerably the free vibration of plates.