This paper presents a two-dimensional model for a planar solid oxide fuel cell (SOFC) anode in order to simulate the steady-state performance characteristics as well as the electrochemical impedance spectra. The developed model couples the mass transport with the electrochemical kinetics. The transient conservation equations (momentum and species equations) are solved numerically and the linear kinetic is used for the anode electrochemistry. In order to solve the system of the nonlinear equations, an in-house code based on the finite volume method is developed and utilized. A parametric study is also carried out and the results are discussed. Results show a capacitive semicircle in the Nyquist plot which is identical to the gas concentration impedance. The simulation results are in good agreement with published data.