The present work investigates the simulation of phase transition in compressible fluids. We postulate a local and instantaneous equilibrium with respect to phasic pressures, temperatures and chemical potentials when both phases are present. This hypothesis leads to the definition of an equilibrium equation of state (EOS) for the two-phase medium. While this thermodynamical assumption is classical, there is no explicit expression of the equilibrium EOS in the general case. We propose simple means to approximate this EOS when both phases are governed by a "Stiffened Gas" EOS. Then we provide an implementation of this method within a Finite-Volume numerical scheme thanks to a two-step relaxation strategy.