An investigation into postbuckling behavior of thin and ultra-thin plates/shells is first performed in this paper. The present formulation is established upon a shell theory using the von Karman assumption and isogeometric analysis (IGA). In the present approach, the bifurcation point in eigenvalue buckling analysis and limit points can be detected simply via the modified Riks method. Hence, eigenvalue buckling analysis and postbuckling analysis are unified in the most simple flowchart. The above advantages allow buckling and postbuckling analyses of ultra-thin, thin and moderate thick plates/shells can be performed directly and conveniently. The obtained results are verified with the reference ones. In addition, the results show that buckling shapes and postbuckling responses of thin structures and ultra-thin structures are significantly different. Effects of slenderness, aspect ratios and curvature on postbuckling response of ultra-thin plates/shells are investigated particularly. Especially, some new results of ultra-thin plates/shells are first provided in this paper.