A gas-to-gas humidifier using membranes is the preferred technology for external humidification of fuel cell reactant gases in mobile applications because no extra power supply is required and there are no moving parts. In particular, a shell and tube structure is compact, which allows its easier integration in a fuel cell vehicle. This paper proposes a mathematical model for the humidifier using the principles of thermodynamics, including analysis of heat and mass transfer and of static and dynamic behaviors. Firstly, the heat and mass transfer behavior was simulated and the results compared with the experimental data. Secondly, the model was used to investigate the sensitivity of the geometric parameters and the effects of various operating conditions on performance. Finally, step responses of the humidifier at various flow rates were analyzed. (c) 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.