The optimal distribution of material to maximize the critical load of columns has been studied extensively in the past, along with initial postbuckling behavior. Here, large postbuckling deflections are analyzed for optimal columns with pinned ends. Small vibrations of the optimal columns about postbuckled equilibrium shapes are also investigated. A shooting method is utilized to obtain numerical solutions. In some examples, an elastic foundation is attached to the column. The foundation includes the usual transverse resistance and an axial resisting force. The bifurcation is subcritical in some cases, and then the column is imperfection-sensitive. Results are compared to those for the corresponding uniform column with the same total volume. © 2009 US Government.