Mathematical modeling plays an important role in fuel cell design. A comprehensive review of the mathematical modeling of proton exchange membrane fuel cells is first conducted. It is found that the results computed by different models in the literature often agree well with the experimental data. This stimulates the present authors to carry out a comprehensive parameter sensitivity examination. In this first paper a three-dimensional, two-phase and non-isothermal model is developed, and numerical simulations for a basic case is performed, the results of which are regarded as the reference for further sensitivity examination. All the parameters needed for the simulation are provided in detail. In the companion paper (Part II), the results of the parameter sensitivity analyses and discussion of model validation are provided in detail. (c) 2006 Elsevier B.V. All rights reserved.