The flexibility index can be used to evaluate process robustness and can be incorporated into algorithms for optimal process design under uncertainty. Traditional approaches to evaluating the flexibility index have focused on explicit enumeration or active set strategies. These necessitate closed form expressions for process constraints and can be computationally expensive to implement for problems with a large numbers of constraints. In addition, these methods generally perform best for problems involving convex or 1-d quasi convex feasible regions with respect to the uncertain variables. In this article, a method for flexibility analysis of systems with black-box constraints will be introduced. This is the second in a series of two articles related to surrogate-based feasibility and flexibility analysis. The first article described a strategy for building surrogate models to represent the feasible region for processes with black-box constraints. In this work, surrogate feasibility functions are used to evaluate the flexibility index for processes that lack closed-form expressions for process constraints. The proposed approach can be applied to processes with stochastic uncertainties described by arbitrary distribution functions. Due to the low computational cost of evaluating surrogate feasibility functions, this method can also be useful for flexibility analysis of processes described by computationally expensive models. The proposed approach will be demonstrated for a series of test problems involving nonlinear, nonconvex and disjoint feasible regions. It will also be applied to evaluate the flexibility of a pharmaceutical roller compaction process with uncertainties described by both uniform and normal distributions. (C) 2015 Elsevier Ltd. All rights reserved.