A fuel cell is a promising energy conversion system that will eventually become the first-choice for producing power because of its clean or zero-emission nature. A steady-state, two-dimensional mathematical model with pressure and phase change effects for a single PEM fuel cell was developed to illustrate the inlet humidification and pressure effects on proton exchange membrane (PEM) fuel cell performance. This model considers the transport of species along the channel as well as water transfer through the membrane. It can be used to predict trends of the following parameters along the fuel cell channels: mole number of liquid water and water vapor, pressure, temperature, density, viscosity, velocity, saturation pressure, pressure drop, vapor mole fraction, volume flow rate, required pumping power and current density.