Design feasibility and flexibility are recognized as important operability characteristics of a chemical process. This is due to the variability of the parameters that appear in process operations and the increasing market environment competition, which requires reliability in meeting product demands and quality specifications. In this work, a novel approach is presented for the evaluation of design feasibility/flexibility based on the principles of the deterministic global optimization algorithm alpha BB (Adjiman, C. S.; Androulakis, I. P.; Floudas, C. A. Comput. Chem. Eng. 1998,22 (9),1159. Adjiman, C. S.; Floudas, C. A. J. Global Optim. 1996, 9, 23-40. Adjiman, C. S.; Dallwig, S.; Floudas, C. A.; Neumaier, A. Comput. Chem. Eng. 1998, 22 (9), 1137. Androulakis, I. P.; Maranas, C. D.; Floudas, C. A. J. Global Optim. 1995, 7, 337), which, in turn, relies on a difference-of-convex-functions transformation and a branch-and-bound framework. The proposed approach can address problems that are described through general nonconvex equality and inequality constraints. A number of examples illustrate the applicability and efficiency of the proposed global optimization framework for both the feasibility test and flexibility index problems.