A new algorithm to find the phase equilibrium conditions in systems with specified values of internal energy, Volume, and number of moles of each component present (isochoric-isoenergetic flash problem) is proposed. The core of the procedure consists of maximizing the system entropy by iterating on the values. in each phase, of internal energy, volume, and number of moles of each component. Analytical expressions for the physical properties and derivatives required by the calculations were generated by computer algebra. The algorithm tests for the possible need to add or remove phases during the course of iterations. The paper discusses possible numerical difficulties during application of the procedure and how to overcome them. The algorithm has shown to be robust and capable of solving multiphase equilibrium problems, avoiding trivial Solutions. (C) 2008 Elsevier B.V. All rights reserved.