Abstract: A planar fuel cell module including a module base unit having a plurality of recesses each adapted to receive a fuel cell therein is described. The recesses can disposed in a linear or two-dimensional planar arrangement. The module base unit also includes a strip conductor for providing electrical connection to the fuel cells. A fuel cell including an anode structure and a cathode structure is received in each of the recesses of the modular base unit. The fuel cells are disposed in each of the recesses such that the fuel cells form fit to a contour of each of the recesses. In some embodiments the anode structure and the cathode structure can be disposed offset at an angle relative to one another and can be accessible from the same side of the fuel cell. A very thin overall arrangement of a fuel cell is provided.