A three-dimensional mathematical model for a planar SOFC was constructed. The concentrations of the chemical species, the temperature distribution, the potential distribution, and the current density were calculated using a single-unit model with double channels of co-flow or counter-flow pattern. The finite volume method was employed for the calculation, which is based on the fundamental conservation laws of mass, energy, and electrical charge. The internal or external steam-reforming, the water-shift reaction, and the diffusion of gases in the porous electrodes were taken into the model., The effects. of the cell size, the operating voltage and the thermal conductivity of the cell components on the calculated results were investigated. From the simulated temperature distributions in the electrolyte and the interconnector, the stress distributions were calculated using the finite element method. The results demonstrated that the steam reforming would generate internal stresses of several tens MPa in an electrolyte.