In the present work we develop, implement, and analyze the results of a new methodology destined to calculate critical points of phase transitions. Our criticality conditions are developed from a slight modification of the Gibbs tangent plane criterion. We formulate the critical points calculation as an optimization problem. Such formulation offers many advantages, among them we can mention the capability of determining more than one critical point, the use of robust numerical methods, and the possibility of visualization of the critical phenomenon from a two-variable (T and P) objective function. To solve the optimization problems we use the simulated annealing algorithm, a stochastic method whose convergence does not depend on initial guesses and gives preference to global optima. Several samples of mixtures were used to test the present methodology. The results of our simulations were compared, in a satisfactory way, with experimental data and with some results calculated in other approaches. (C) 2004 American Institute of Chemical Engineers.