A steady-state and three-dimensional (3-D) model has been established for an intermediate temperature planar anode-supported solid oxide fuel cell. The model couples charge transfer, mass transfer, momentum transfer, and energy transfer equations. Chemical reactions (methane cracking reaction (MCR), Boudouard reaction, methane steam reforming reaction (MSR), and water gas shift reaction (WGSR)) and electrochemical oxidation of H-2 and CO are considered. The variations of carbon activity, fuel utilization, and temperature distribution have been discussed with polarization and concentration separately. The thermal stress distribution in the positive electrode-electrolyte-negative electrode (P-E-N) structure is also discussed. The simulation results agree well with the literature.