This article presents a new framework, based on parametric programming, that unifies the solution of the various flexibility analysis and design optimization problems that arise for linear, convex, and nonconvex, nonlinear systems with deterministic or stochastic uncertainties. This approach generalizes earlier work by Bansal et al. It allows (1) explicit information to be obtained on the dependence of the flexibility characteristics of a nonlinear system on the values of the uncertain parameters and design variables; (2) the critical uncertain parameter points to be identified a priori so that design optimization problems that do not require iteration between a design step and a flexibility analysis step can be solved; and (3) the nonlinearity to be removed from the optimization subproblems that need to be solved when evaluating the flexibility of systems with stochastic uncertainties.