In this paper. we propose a new method for phase stability analysis with cubic equations of state by minimization of the tangent plane distance (TPD) function. A global optimization method called tunneling, able to escape from local minima and saddle points is used here. The tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the TPD function. In phase two (tunneling), either global optimality is ascertained. or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The tunneling method is used for the conventional approach, and for the reduced variables approach. In the latter case, the number of independent variables does not depend on the number of components in the mixture. The solution of the minimization of TPD function should be found in a space with a significantly reduced number of dimensions. The new method is used for testing phase stability for a variety of representative systems. The examples show the robustness of the method even in the most difficult situations. The proposed method is more efficient than other global optimization methods. Furthermore, in many cases, the reduced approach is faster than the conventional approach. The results showed the efficiency and reliability of the novel method for solving the global stability problem.