The aim of the work was to develop a mathematical model for computing the steady-state voltage – current characteristics of a planar Solid Oxide Fuel Cell and to determine the performance of a new SOFC design. The design involves cross-flow bipolar plates. Each of the bipolar plates has an air channel system on one side and a fuel channel system on the other side. The proposed model was developed using the ANSYS-Fluent commercial Computational Fluid Dynamics (CFD) software supported by additional Fuel Cell module. The results confirm that the model can well simulate the diagonal current path. The effects of temperature and gas flow through the channels and a Membrane Electrode Assembly (MEA) structure were taken into account. It was shown that a significant increase of the MEA temperature at high current density can lead to hot spots formation and hence electrode damage.