Process uncertainty is almost always an issue during the design of chemical processes (CP). In the open literature it has been shown that consideration of process uncertainties in optimal design necessitates the incorporation of process flexibility. Such an optimal design can presumably operate reliably in the presence of process and modeling uncertainty. Halemane and Grossmann (1983) introduced a feasibility function for evaluating CP flexibility. They also formulated a two-stage optimization problem for estimating the optimal design margins. These formulations, however, are based implicitly on the assumption that during the operation stage, uncertain parameters can be determined with enough precision. This assumption is rather restrictive and is often not met in practice. When available experimental information at the operation stage does not allow a more precise estimate of some of the uncertain parameters, new formulations of the flexibility condition and the optimization problem under uncertainty are needed. In this article, we propose such formulations, followed by some computational experiments.