The determination of critical points of mixtures is important for both practical and theoretical reasons in modeling phase behaviour; especially at high pressure. This article presents the first completely reliable method for locating all the critical points of a given mixture. The method also verifies the nonexistence of a critical point if a mixture of a given composition does not have one. The methodology used is based on interval analysis, in particular an interval Newton/generalized bisection algorithm providing a mathematica and computational guarantee that all mixture critical points are located. The procedure is initialization-independent and thus requires no a priori knowledge of the number of mixture critical points or their approximate locations. The technique is illustrated using several example problems involving cubic equation-of-state models; however, the technique is for general purpose and can be applied in connection with other thermodynamic models.