In this paper, we consider the solution of process optimization models under uncertainty (two-step optimization or TSOP). We note that the design variables found by solving the TSOP can guarantee the flexibility of chemical processes only if the solution corresponds to a global minimum. Therefore, we discuss the conditions under which a global minimum is obtained by selected deterministic methods available in the open literature. It should also be noted that for practical problems, it is often very difficult to check convexity (concavity) conditions which are often considered in flexibility analysis. To address this problem, two modifications of a method due to Ostrovski and Volin (1997) are suggested. These modifications extend the class of problem for which the global solution can be obtained.