The main purpose of this research is study of the elastic and inelastic local buckling of rectangular plates with centerline boundary conditions. The Galerkin method is used to establish an eigenvalue problem and buckling coefficients are obtained by using trigonometric and polynomial functions that satisfy the boundary conditions. In elastic local buckling case study, plates are subjected to non-uniform in-plane compression. Also solutions for tapered thickness plates and plates subjected to shear stress are presented. The solution is developed to inelastic local buckling and by using of Galerkin method a solution for rectangular plates is presented. Results of the research are applicable to stiffened plates and I-shaped beams that are subjected to biaxial bending or combined flexure and torsion, and important to estimate the reduction in elastic buckling capacity due to stress gradient.
