Phase stability testing is an important subproblem in phase equilibrium calculations. Phase stability analysis consists in finding either all stationary points or only the global minimum of the tangent plane distance (TPD) function. The TPD surface is non-convex and may be highly non-linear, and many phase stability calculations are rather difficult. in this work we are solving the phase stability problem using the tunneling global optimization method and a modified objective function; all stationary points of the TPD function are global minima of this objective function. For finding all its global minima at the same level (known, with objective function equal to zero), we exploit a unique feature of the tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Numerical experiments for various difficult phase equilibrium problems show that the tunneling method is a powerful and reliable tool for global phase stability testing. (C) 2009 Elsevier B.V. All rights reserved.