This study reports a two- dimensional numerical simulation of a steady, isothermal, fully humidified polymer electrolyte membrane ( PEM) fuel cell, with particular attention to phenomena occurring in the catalyst layers. Conservation equations are developed for reactant species, electrons and protons, and the rate of electrochemical reactions is determined from the Butler - Volmer equation. Finite volume method is used along with the alternating direction implicit algorithm and tridiagonal solver. The results show that the cathode catalyst layer exhibits more pronounced changes in potential, reaction rate and current density generation than the anode catalyst layer counterparts, due to the large cathode activation overpotential and the relatively low diffusion coefficient of oxygen. It is shown that the catalyst layers are two- dimensional in nature, particularly in areas of low reactant concentrations. The two- dimensional distribution of the reactant concentration, current density distribution, and overpotential is determined, which suggests that multi- dimensional simulation is necessary to understand the transport and reaction processes occurring in a PEM fuel cell.