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This paper deals with a nonlinear static plate model based on Berger theory, which is a specific case of a generalization of the Woinowsky-Krieger mathematical model of beam bending. It is considered a plate bending with forces acting in the middle plane of the plate and a contact problem with an elastic foundation, where the normal compliance condition is employed. A variational equation of the problem and a functional of the total potential energy corresponding to the variational equation are derived. Under additional assumptions on the data (e.g., clamped plate), the existence and uniqueness of the solution are proved. A numerical solution is based on the Galerkin method and Courant approximation. The theory is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]