The main purpose of operational flexibility analysis is to determine and describe the flexibility region. The existing methods are mainly developed by numerical calculation methods to estimate the contour of the flexibility region. In this article, a novel method is proposed for solving operational flexibility models described by polynomials. The proposed method can accurately describe the flexibility region and explicitly express the functional relationships between uncertain parameters and control variables. First, the original flexibility analysis model is represented as an existential quantifier formula. Then, a technique of quantifier elimination is introduced to deduce the formula to a series of explicitly triangular quantifier-free formulas. Last, a logical combination of the quantifier-free formulas can be used to depict the complete flexibility region. The case studies show that the deduced explicit expressions can accurately and effectively describe the flexibility region and guide the steady-state control operations, regardless of convex or nonconvex systems. (C) 2018 American Institute of Chemical Engineers