A new nano-scale plate-like model in which the influence of surface effect and the geometrically nonlinear condition are considered is introduced on the basis of Mindlin theory. By using Hamilton's principle, the governing equations are derived. The residue membrane force and bending moment, which are caused by the surface stresses, are explicitly expatiated. After analyzing the membrane force and bending moment, it can be obtained that they are dependent on the deformation of the film and are accordant to classical plate theory. The model is then applied to analyze the bending and buckling of simply supported micro- and nano-films in plane strains . Differing from the conventional plate theory, the proposed model and solutions involve the intrinsic scale and depend on the thickness of the film. Thus, it can be found that when the thickness of,the film is equal to or less than the intrinsic scale, the surface effect is strongly sensitive to the thickness of the film.