A computational procedure for construction of approximate phase boundaries without iterative determination of equilibrium phase compositions has been developed. The method, which is very easy to implement, reduces the equilibrium conditions for mixtures containing an arbitrary number of components to only two equations to be solved for temperature and pressure. In addition a refinement procedure is described for exact calculation of points on the phase boundary, which enables fast convergence in the critical region without the requirement for composition derivatives of the component fugacity coefficients.