This paper presents a methodology for the prediction of the dispersion of a two-phase release from a chemical or process plant. A set of one-dimensional conservation equations for modelling such a release is derived, by taking an approach analogous to the boundary-layer integral method, in which the instantaneous conservation equations are averaged over a volume slice transverse to the direction of predominant plume/cloud motion. Averaging, which makes the problem computationally tractable, removes information regarding local gradients that govern transport of momentum, heat and mass - this information must then be supplied in the form of ＇closure relationships＇. An appropriate set of closure relationships is then discussed, covering models for interfacial heat and mass transfer, entrainment of air, and interactions with the wind field. Particular features of the approach are that it is flexible enough to deal with condensation of water vapour, thermal non-equilibrium between the phases, sloping terrain, and can handle both elevated and ground-bounded releases. Suitable formulations for the initial and source boundary conditions, for both instantaneous and continuous releases, are also presented.