In the design of chemical processes, such as catalytic cracking of bitumen and heavy oil, the knowledge of phase behavior at the critical endpoint is essential. Based on the PR equation of state, the algorithm developed by Heidemann and Khalil for calculating critical properties was used to compute critical points. An algorithm for determining the equilibrium phase of the critical point using the tangent plane criterion was developed, and was used to calculate the critical endpoints of different mixtures, including non-polar, polar and associating systems. The critical endpoint, representing the type of the phase behavior, was employed to fit the interaction parameter of mixtures in critical state at high pressure. Lines of critical endpoints for ternary mixtures were also determined with the algorithm.