This paper describes an efficient two- and three-phase flash calculation algorithm for equation of state (EOS) compositional reservoir simulation problems. In this approach, two sets of linear equations with the same coefficient matrix are established on the basis of the phase equilibrium information at the previous time step. The solution of these equations is the distribution of mole number of each component between phases. The phase saturation can thus be obtained without solving the Rachford-Rice equation. A number of reservoir simulations have been performed to show the validity of the new algorithm. Comparisons are made of these runs with those conducted by a rigorous fugacity iteration method. No apparent difference in the results from the two methods is observed. However, the CPU time can be significantly saved by using the new approach, generally around 50%. In this work an attempt is also made to employ the non-iterative approach as a tool for providing the initial guess for the rigorous EOS iteration. A considerable reduction of the CPU time is again observed.