For an anode-supported planar SOFC, a single-unit with double channels was modeled for a counter-flow pattern, and the concentration polarization at the anode was estimated. The flow phenomena were simulated using the finite volume method and the distribution of the gaseous species was calculated. In the model, it was assumed that the gas flow in the porous anode is governed by Darcy's Law, and the reactant species are transported to the electrolyte/anode interface mainly by diffusion in a multicomponent mixture system. For binary H-2-H2O and CO-CO2 systems, the calculated concentration polarization was found comparable to the experimental results. As an example for a multicomponent system, a model using steam-reformed methane as a fuel was employed to simulate the concentration polarization at a high fuel utilization. From the simulated results, it was evident that the shift reaction effectively reduces the concentration polarization when the fuel utilization is high.