This article presents a rigorous mathematical model to predict performance of proton exchange membrane (PEM) fuel cells (FCs) of arbitrary three-dimensional (3-D) geometry. Mathematical modeling of FCs is necessary in order to understand the precise effect of operating conditions and material properties on the performance of fuel cells. The model is based on solution of the conservation equations of mass, momentum, energy, species, and electric current in a fully integrated finite-volume solver. Simulations are performed in 2-D and 3-D geometries assuming that water stays in its vapor phase and that no liquid water is formed. Results are compared against experimental data under various operating conditions, and show that 3-D modeling is key to predicting performance of PEM FCs at high current densities. (C) 2003 The Electrochemical Society.