Flexibility and stability are key components of chemical process operability and are important in practical applications. In previous research, flexibility and stability have been studied separately, resulting in flexible regions containing unstable parts that should be avoided in terms of operability. This paper considers flexibility and stability simultaneously, with the aim of obtaining a stable flexible region for the process. On the basis of existing algorithms for flexibility analysis, the vertex algorithm and active constraint algorithm are presented for the simultaneous analysis of flexibility and stability. Certain limitations of these algorithms are explored and discussed. Then, using the eigenvalue optimization method, we propose a new formulation of the simultaneous analysis of process flexibility and stability. Case studies of the methyl methacrylate polymerization and 1,3-propanediol fermentation are provided. The obtained results illustrate the need to consider flexibility and stability simultaneously and demonstrate the effectiveness of the novel method presented in this paper.