Aspects of postbuckling behavior are investigated for structures undergoing plastic deformation. The structures singled out are characterized by a highly imperfection-sensitive behavior where buckling takes place in the elastic range. A simple model study is carried out and is followed by an analysis of the plastic buckling of a complete spherical shell under external pressure. In both instances, the bifurcation behavior and subsequent deformation of the perfect structure as well as the influence which geometric imperfections have on buckling are studied.