A novel solution approach that addresses uncertainty, flexibility evaluation and design of linear processes is presented based on sensitvity analysis and linear programming. The idea is to evaluate the flexibility index of a process by successively expanding within a bounding search procedure a hyper-rectangle around a nominal point in the uncertainty parameter domain, thus expanding the limits of feasibility for an existing design. Sensitivity information, derived from the solution of a special form of the embedded min-max problem, is utilized for the identification and investigation of the supporting active sets. Since the proposed approach automatically generates all the supporting active sets, it is incorporated within a design model for automatically generating flexibility constraints. As demonstrated by example problems, this approach identifies all critical points that limit flexibility, including multiple equidistant points, without enumerating (explicitly or implicitly) all possible active sets, and considering only the supporting active sets. Therefore, it offers an efficient and constructive way for the evaluation and design of linear processes.