A computer code, MNODE, for predicting the state histories and inventories of an inert gas and water liquid and vapor flowing in a zoned containment has been developed. It employs a model that describes the unsteady flow and thermodynamics of two-phase two-component mixtures flowing among 12 connected control volumes. This calculational model can be applied to problems of hypothetical high-pressure primary coolant, feed water, or steam line ruptures in such structures as nuclear containments, tunnels, or auxiliary buildings. In comparison with previously reported zoned containment computation models, this model rigorously treats the thermodynamics of two-phase two-component mixtures of water and an inert gas, is provided with several flow model options including an inertia flow equation, and is demonstrated with substantial verification. Predictions are compared with the results of an analytical gas dynamic problem, semiscale blowdown experiments, and solutions to a subcompartment analysis standard problem by other computer codes in use within the nuclear industry.