Abstract: In this paper, the equations of motion for a monolayer graphene are obtained by a continuum limit form of elastic energy of the Lenosky C-C covalent bond and Hamilton principle. Using the equations and Galerkin method the static bending of a rectangular monolayer graphene is investigated. It is found that the bending stiffness has a significant effect on the Mechanical Characteristics of the grapheme. The graphene may be described by a plate when the graphene size is small, but the effect of bending stiffness will quickly decrease accompanying the size increment of the graphene. When the short side dimension is greater than 10nm for a rectangular monolayer graphene, the bending stiffness may be neglected and a thin film model is a good agreement with the monolayer graphene.