In this paper, formulation of an elastic-plastic large displacement theory of the “Idealized Rectangular Plate Element” and the “Idealized Stiffened Plate Element” is carried out. In this formulation, local (inter-unit) nonlinearities (large deflection, buckling and plasticity) as well as overall nonlinearities are taken into account. On the local level, behaviour of plates and stiffened plates is idealized according to the techniques of the Idealized Structural Unit Method. On the global level, plates and stiffened plates are treated as membranes neglecting their out-of-plane bending contribution to the global structure in comparison with their inplane contribution and the contribution of primary supporting members. Out-of-plane as well as inplane large displacements of the global structure are taken into account. The process of the formulation is presented and the validity of this approach is theoretically demonstrated. The problem of coupled local and global buckling of box columns is demonstrated through results of analysis of an example box column. Results of analysis of coupled web buckling and lateral buckling of I girder are also presented.