A flow model is built to capture evaporating interfaces separating liquid and vapour. Surface tension, heat conduction, Gibbs free energy relaxation and compressibility effects are considered. The corresponding flow model is hyperbolic, conservative and in agreement with the second law of thermodynamics. Phase transition is considered through Gibbs energy relaxation, in the same mind as in Saurel et al. (2008). Surface tension effects are modelled following the lines of Brackbill et al. (1992). There is thus no need to resolve the interface structure as jump conditions are inherent features of the model formulation. With the present approach, the same set of partial differential equations is solved everywhere, in pure fluids as well as in the captured diffuse interface. There is thus a unique hyperbolic flow solver that handles flow dynamics, interface motion and eventually acoustic wave dynamics. To make distinction between “pure” fluids and liquid–vapour mixture treatment, different sets of algebraic equations are considered in the relaxation solver. To guarantee accurate computation of the liquid and gas dynamics the preconditioned implicit scheme of LeMartelot et al. (2013) is adapted to the present boiling flow model. The model and method are validated against a one-dimensional test problem having exact solution. Multidimensional computations are then shown to illustrate method capabilities.