In this work we present a nonlinear lumped parameter model of the airway/lung mechanics. The model is able to reproduce the time evolution of the fundamental variables (pressure, flow and volume) within each compartment of the respiratory system during normal breathing. A particular attention is given to the pleural pressure that is the driving force of the system. Our purpose is to build a tool for a qualitative description of the lung/airway dynamics that is able to reproduce the physiological behavior of the main system variables. The aim of this work is to develop a model of the respiratory system and successively insert it into our numerical lumped parameter model of the cardiovascular system. In this way it will be possible to study the interactions between the cardiovascular, the respiratory system and the most used mechanical circulatory and ventilatory assist devices in terms of hemodynamic and energetic variables.