The prediction of outflow from high pressure vessels or pipework following an accidental failure is required in the safety assessment of industrial plant used to process or store flammable material. In particular, predictions of the mass flow rates of accidental leaks provide source conditions for mathematical models of gas dispersion or accumulation and fires. In this paper, the modelling of outflow from high pressure vessels in the context of the development of a safety assessment package is addressed. For any consequence model implemented as part of a safety assessment package, the issues of model robustness and efficiency as well as accuracy must be considered. The outflow model described in this paper is demonstrated to predict the mass flow rate for releases into the atmosphere from high pressure vessels accurately in a fast and robust manner. The mathematical formulation of the model, the numerical methods used to implement the model and its validation are discussed.