Procedures for the numerical computation of an index for operational flexibility in chemical processes are considered. Two types of algorithms are proposed which rely on the assumption that critical points for feasible operation lie at vertices or extreme values of the uncertain parameters. The first algorithm is a direct search procedure that features a heuristic variant to avoid exhaustive enumeration of all vertices. The second algorithm employs an implicit enumeration scheme based on a lower bound for monotonic constraints. These algorithms are applied to several example problems to demonstrate both the use of the flexibility index in process design and the computational efficiency of the algorithms.