The contact problem of an inflated spherical nonlinear elastic membrane between two large rigid plates is formulated in terms of three first-order ordinary differential equations for the region where the spherical membrane is not in contact with the rigid plates. The constraint condition introduced by the rigid plate on part of the spherical membrane reduces the number of governing equations to two for the contact region. A general stress-strain relation for the spherical membrane is used in the formulation. The results presented in this paper assume that the material behavior of the spherical membrane is that described by the Mooney model. Nonlinear spring characteristics and the instability phenomena of the inflated membrane are discussed.