In this study we propose a method for phase stability analysis at pressure and temperature specifications, in the frame of a "volume-based thermodynamics. The formulation of the tangent plane distance (TPD) criterion in terms of the Helmholtz free energy is used in this work for testing phase thermodynamic stability at p - T conditions, using component molar densities as primary variables. The phase stability problem is non-convex; the TPD function may exhibit multiple local minima and saddle points, the use of global optimization methods for its minimization being appropriate. For the unconstrained minimization of the TPD function we use the tunneling global optimization method, which has shown its ability in efficiently solving difficult non-convex, highly nonlinear problems. The method is tested for a variety of mixtures ranging from binaries to mixtures with many components, with emphasis on difficult conditions. The proposed method proved to be an efficient and reliable tool for phase stability analysis.