Abstract <p>Three-phase flow is commonly present in oil and gas production pipelines. Three-fluid models are extensively used for numerical simulation. Accurately modeling and solving the three-phase flow model is fundamental for monitoring the flow parameters and ensuring production stability. However, the model may be ill-posed under certain initial conditions. No reliable methods have long been used to judge the well-posedness of three-fluid models. This study presents a universal method for determining the well-posedness of the three-fluid model, which can judge the model’s well-posedness of single-phase, two-phase, and three-phase flow under the stratified flow pattern. The model’s well-posedness range in the subsonic region becomes notably limited under the high pressure and the large fluid density ratios. A convenient eigenvalue map method with a wide range of liquid holdup and pressure to analyze the three-fluid model’s hyperbolicity is proposed, which can intuitively describe the well-posed range of the model under typical operating conditions and the distribution of model eigenvalue signs, as well as determine the boundary parameters on the pipelines' inlet and outlet boundaries. The three-fluid model has the largest well-posed range under low pressure and low liquid holdup. The proposed method provides a reference for well-posed analysis and accurate solution of the three-fluid model.</p>