This paper describes a finite-difference computational method suitable for the simulation of vapor–liquid (or gas–liquid) flows in which the dynamical effects of the vapor can be approximated by a time-dependent, spatially uniform pressure acting on the interface. In such flows it is not necessary to calculate the velocity and temperature fields in the vapor (or gas). This feature simplifies the solution of the problem and permits the computational effort to be focussed on the temperature field, upon which the interfacial mass flux is critically dependent. The interface is described by a level set method modified with a high-order ‘‘subcell fix’’ with excellent mass conservation properties. The use of irregular stencils is avoided by suitably extrapolating the velocity and temperature fields in the vapor region. Since the accurate computation of momentum effects does not require the same grid refinement as that of the temperature field, the velocity field is interpolated on a finer grid used for the temperature calculation. Several validation and grid refinement axi-symmetric tests are described which demonstrate the intended first-order time, second-order space accuracy of the method. As an illustration of the capabilities of the computational procedure, the growth and subsequent collapse of a laser-generated vapor bubble in a microtube are described.