We present an isothermal model for liquid-vapor phase transition. We use a Hamilton principle to derive the conservative part of the system and we propose additional stiff phase change source terms that are compatible with the second thermodynamic principle. These terms are considered as relaxation terms and define an equilibrium manifold for the system. We formally study the equilibrium return process. While the original system is hyperbolic, the equilibrium limit system is only weakly hyperbolic. Finally, we propose a numerical scheme based on the relaxed system.