A three-dimensional computational fluid dynamics model was developed to study the performance of a planar solid oxide fuel cell (SOFC). The governing equations were solved with the finite volume method. The model was validated by comparing the simulation results with data from literature. Parametric simulations were performed to investigate the coupled heat/mass transfer and electrochemical reactions in a planar SOFC. Different from previous two-dimensional studies the present three-dimensional analyses revealed that the current density was higher at the center along the flow channel while lower under the interconnect ribs, due to slower diffusion of gas species under the ribs. The effects of inlet gas flow rate and electrode porosity on SOFC performance were examined as well. The analyses provide a better understanding of the working mechanisms of SOFCs. The model can serve as a useful tool for SOFC design optimization.