Methods for multiphase equilibrium calculations are generally based on Gibbs free energy minimization or equation-solving. Equation-solving methods, although superior to free energy minimization methods for phase equilibrium calculations without chemical reactions, often involve sequential procedures for a priori phase identification. A simultaneous equation-solving method (tau-method), based on modifying mole fraction summations, is proposed for these calculations. It requires the solution of a minimization problem only once, and provides phases actually present at equilibrium, their quantities and compositions simultaneously; and phase identification in advance is not required. Phase characteristic variable and pseudo phase are introduced, and their significance discussed. tau-method is shown by analysis and numerical results, to be consistent with Nelson＇s (1987, Comput. Chern. Engng 11, 581-591) criteria for phase existence. The method is tested on typical examples for two-phase (vapor-liquid and liquid-liquid) and three-phase (vapor-liquid-liquid) equilibrium calculations. For each example, several conditions and/or different initializations are used, and the minimization problem is solved by a version of successive linear programming method. The results show that tau-method is successful and reliable for multiphase equilibrium calculations.