A flow model is derived for the numerical simulation of interfacial flows with phase transition. The model arises from the classical multi-component Euler equations, but is associated to a non-classical thermodynamic closure: each phase is compressible and evolves in its own subvolume, with phases sharing common pressure, velocity and temperature, leading to non-trivial thermodynamic relations for the mixture. Phase transition is made possible through the introduction of Gibbs free energy relaxation terms in the equations. Capillary effects and heat conduction—essential in boiling flows—are introduced as well. The resulting multi-phase flow model is hyperbolic, valid for arbitrary density jumps at interfaces as well as arbitrary flow speeds. Its capabilities are illustrated successively through examples of nozzle induced cavitation and heated wall induced boiling.