A generalized Reissner theory for axisymmetric problems of circular plates is presented. The plate is assumed to be linearly elastic, and large rotations and strains are allowed. Shear deformation and changes in the plate thickness are neglected. Equilibrium equations are formulated, and a shooting method is applied to obtain numerical results for plates subjected to a uniform pressure. The edge of the plate is assumed to be either simply supported or clamped, and is free to move radially. The resulting deflections are compared to those based on the von Kármán theory.