The once-through heat recovery steam generator (HRSG) design is ideally matched to very high temperature and pressure, well into the supercritical range. Moreover this type of boiler is structurally simpler than a conventional one, since no drum is required. In a conventional design, each tube plays a well-defined role: water preheating, vaporisation, superheating. Empirical equations are available to predict the average heat transfer coefficient for each region. For once-through applications, this is no more the case and mathematical models have to be adapted to account for the disappearance of the conventional economiser, boiler and superheater. General equations have to be used for each tube of the boiler, and the actual heat transfer condition in each tube has to be identified. The mathematical complexity as well as the number of equations is increased. A thermodynamic model has been selected and implemented to suit very high pressure (up to 240 bar), sub- and supercritical steam properties. Model use is illustrated by two case studies: a 180 bar once-through boiler (OTB) and a conventional boiler superheater and reheater.