In this chapter two approaches have been adopted to adequately simulate the transport phenomena occurred in a Solid Oxide Fuel Cell (SOFC). The first one is a one dimensional, relatively simple model, providing a rather simple and stable solution by using analytical manipulations and combined numerical techniques. The other is a three-dimensional approach including the coupled solution for flow, heat transfer, mass transport and electrochemistry. It is found that higher fuel consumption corresponds to higher current density values in an equivalent manner. Furthermore, it is clearly depicted that the overpotential increases along the anode, resulted by the consequent increment of the fuel consumption with the distance. Finally, the overpotential increases with current density, which is in accordance with previously presented experimental and theoretical results.