Engineers agree with the fact that uncertainty is an important issue to get a better model of real behavior. Uncertainty quantification techniques have been largely developed during the recent years; Stochastic and probabilistic collocation methods are clear examples of recent developments. This work is based on a more traditional uncertainty quantification method, as Monte-Carlo method and its extension to Latin Hypercube sampling techniques. Two definitions of the optimization problem have been analyzed. The first one is the called Stochastic procedure, while the second one is the Robust one. Both of them deal with uncertainty on the input parameters, but they manage the uncertainty effects from two different points of view. Applications to aerodynamics and aero-elastic problems have been described.