Phase equilibrium calculations are often involved in the design, simulation, and optimization of chemical processes. Reported methods for these calculations are based on either equation-solving or Gibbs free energy minimization approaches. The main objective of this work is to compare selected methods for these two approaches, in terms of reliability to find the correct solution, computational time, and number of K-value evaluations. For this, four equation-solving and three free minimization methods have been selected and applied to commonly encountered vapour-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE), and vapour-liquid-liquid equilibrium (VLLE) examples involving multiple components and popular thermodynamic models. Detailed results show that the equation-solving method based on the Rachford-Rice formulation accompanied by mean value theorem and Wegstein's projection is reliable and efficient for two-phase equilibrium calculations not having local minima. When there are multiple minima and for three-phase equilibrium, the stochastic method, genetic algorithm (GA) followed by modified simplex method of Nelder and Mead (NM) is more reliable and desirable. Generic programs for numerical methods are ineffective for phase equilibrium calculations. These findings are of interest and value to researchers and engineers working on phase equilibrium calculations and/or developing thermodynamic models for phase behaviour.