The inspiratory pump (inspiratory muscles and the rib cage) translates inspiratory commands in alveolar ventilation by applying expanding forces to the lungs. Its functioning is of paramount importance to the physiology of breathing and of many pathological situations. Major difficulties in studying its function in relationship with its structure arise from the extremely complex geometrical disposition of its active and passive elements. We herein describe a two-compartment model of the inspiratory pump, with model parameters identification derived from actual measurements obtained by magnetic resonance imaging in normal humans. The equations governing the model are presented. Numerical simulations validate the model by showing a behaviour similar to physiological observations. This opens the possibility of predicting the behaviour of the respiratory system during diseases involving changes in its mechanical or geometrical characteristics.