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The purpose of the paper is twofold, first to suggest a general method, called the second variation-convex analysis mixed method, for analysis of nonlinear functionals. As an application of the approach, a strictly dual complementary variational principle of Reissner plates with the local form1 and the existing criterion of variational solution have been studied. The study shows that the principle and the criterion1 can be improved into a global form by using the novel approach. In contrast with existing methods (Jin1 and Gao and Stang2), this method will be able to analyze general nonlinear problems,1 rather than geometrically nonlinear ones.2 Our second purpose is to present a new approach to the derivation of the exact boundary integral equation for the analysis of nonlinear Reissner plates and to the derivation of the criterion for the solution of the boundary integral equation. Subsequently, the boundary and the domain of the plate are discretized to solve the nonlinear problems. All unknown variables are at the boundary. Numerical results are presented to illustrate the method and demonstrate its effectiveness and accuracy.