Current flare and jet fire models used in the process industry are primarily based on hydrocarbon gases and have been found not to be particularly effective for low luminosity gases such as hydrogen and syngas mixtures. This article presents a new model for such gases, for low to high pressure releases in both vertical and horizontal orientations. The model, which predicts flame geometry and thermal radiation, allowing for jet momentum, buoyancy, wind and flame radiant fraction, is based on extension of established models, with the addition of several new correlations. Validation against existing published data and new previously unpublished test data collected at both pilot and full scale is presented. This article provides the complete set of equations for the model. (c) 2016 American Institute of Chemical Engineers Process Saf Prog 36: 237-251, 2017