A simple aeroelastic structure possessing uncertain elastic modulus, which is modeled as varying either in a convex hull of experimental data points or within an approximating ellipse of minimum area containing all of the data, is studied. A solution of an antioptimization problem, which is dee ned as the search for the worst critical velocity under uncertainty constraint is determined. At the second stage, the optimization problem is addressed as an evaluation of the design variables, such that the worst critical velocity is made to exceed a preselected velocity. It appears that, due to the unavoidable presence of uncertainties, realistic aeroelastic problems ought to be posed as a hybrid optimization and as antioptimization procedures. Several numerical results are elucidated to illustrate the ideas.