Heat and Moisture Exchanger (HME) is a simple solution to the problems of warming and humidification of inspired gases during ventilator treatment. The device acts as an "artificial" nose or passive humidifier, added to the breathing circuit to retain and exchange heat and moisture between inspiration and expiration. The HME traps expiratory heat and moisture from patient's exhaled breath in a porous medium and returns a portion of them through the subsequent inspiratory cycle. The aim of our paper is to develop a computational fluid dynamics (CFD) model of an HME device commonly used in anaesthesia and intensive care. The CFD results allow a better understanding of flow behaviour leading to the design of more efficient devices. The CFD model solves the gas flow, heat and mass transfer equations in a DAR Hygrobac S (Mallinckrodt DAR, Mirandola, Italy). The temperature, absolute humidity and pressure fields are obtained during expiratory phase to evaluate heat and moisture conserving efficiencies and air flow resistance. The effect of flow rate as one of the major parameters in ventilator setting on temperature, humidity and pressure drop is determined. Inside the HME device, areas of recirculation are observed. As the flow rate increases the output temperature and absolute humidity go up causing a reduction in heat and moisture conserving capacities. Comparison of the CFD results with previously obtained experimental data shows a satisfactory agreement.