This chapter provides an introduction to the structure, function, and mechanics of the respiratory system, before proceeding to discuss existing models in the literature that have been developed to answer a variety of questions on respiratory performance. The procedure of developing a validated lumped parameter mathematical model of a non-linear biological system such as the lung is described, and its implementation in the Simulink™ environment is also elaborated on. This is followed by an explanation of how such a model can be integrated with a model of a respiratory device (such as the Bubble CPAP system developed in Chapter 8) to determine the effect of device operation on respiratory performance. In particular, the model is used to study the transmission of pressure oscillations in combination with Continuous Positive Airway Pressure (CPAP) through the neonatal tracheobronchial tree.