An analytical model is described which predicts the performance of a pyrotechnic airbag inflator by accounting for the heat transfer, filtration, combustion, fluid flow and thermodynamic processes occurring during operation. The dynamic system has many interrelationships among the variables describing these processes and also their histories. A detailed energy accounting highlights the role of the filter as a heat exchanger. The role of filter clogging is also discussed. The nonlinear variation of tank pressure with mass of gas generating material is explained, as is the phenomenon where inflators having similar tank pressures produce different airbag pressures even in an unvented airbag.