This paper develops a “power-series” method which may be applied to the bending and buckling, of long, thin, rectangular plates when the deflection and curvature are large and the loading is a function of the transverse coordinate only. The method depends upon the constancy of a certain quantity, N + M2/2, whenever the loading is continuous. The condition of continuity may be removed and the results applied to any general loading. Explicit expressions, to any degree of accuracy, are obtainable for the bending moment, transverse force, and deflection. The method is applied to verify the theory of bending of a plate under uniform load, edges clamped or pinned. The problem of the elastica and the effect of discontinuous loads are discussed briefly.