In this paper, we advocate the use of the Tunnelling global optimization method for phase stability analysis and for multiphase equilibria calculations. The method had been successfully used for solving a variety of phase-equilibrium problems. The Tunnelling method has two steps. First, a minimum (which may not be the putative global minimum) of the objective function is found by a local bounded minimization algorithm. In a second step, the method checks for global optimality. If the minimum found in the first step is only a local minimum, a feasible initial estimate for a new minimization is generated in another valley of the objective function. Cubic equations of state are used, but any thermodynamic model for the Gibbs free energy can be used (the method being model-independent). The proposed method has,proven to be an efficient and reliable tool for multiphase equilibrium calculation.