This paper presents a complete polarization model of a solid oxide fuel cell (SOFC) that eliminates the ambiguity of the suitability of such model when used under different design and operating conditions. The Butler–Volmer equation is used in the model to describe the activation overpotential instead of using simplified expressions such as the Tafel equation and the linear current–potential equation. In the concentration overpotential, both ordinary and Knudsen diffusions are considered to cater for different porous electrode designs. Sensitivity tests are then conducted to show the effect of the thickness of the respective fuel cell components on the drop in cell voltage. Results show that the performance of an anode-supported fuel cell is superior to that using cathode as the support under elevated operating pressure in the cathode compartment. The former can achieve an improved operating range of current density under normal atmospheric conditions.