The Bureau of Mines developed a mathematical model that describes the interaction of an automated breathing and metabolic simulator, or lung, with a self-contained self-rescuer that is supplied compressed oxygen. The model can be used to predict the gas partial volumes of o2, n2, and co2 in the lung and in the self-rescuer breathing bag for a prescribed metabolic state that characterizes the lung. Nonlinear rate equations are used to describe the temporal evolution of the gas partial volumes. A numerical procedure was established with a Fortran computer program to solve these equations, which correspond to a given metabolic state. Examples are presented of applications of the model to predict bag volume and bag oxygen concentration changes with time when the bag is controlled by an automated breathing simulator. Under certain restrictive conditions, the model equations can also be used to analytically predict the time required for the bag to reach a maximum or minimum volume. The model equation in this latter case was extended to transitions between metabolic states, with transitions described as exponential growth or decay processes.