The invention relates to a fuel cell stack with a plurality of plate shaped fuel cells. Each fuel cell provides an electrolyte layer, an adjacent electrode and cathode. The fuel cells are connected mechanically and electrically by bipolar plates. Tightness is ensured in an improved manner. The fuel cells provide a cathode, an anode and an electrolyte layer arranged between the cathode and anode. Each cathode is adjacent to a cathode chamber and each anode is adjacent to an anode chamber. The bipolar plates comprise first openings which are used to provide channels to allow operating material to be transported to the fuel cells or to enable the removal of depleted operating material. The bipolar plates have additional openings, in which the fuel cells are arranged. When the fuel cell is disposed in the opening, it is only substantially and openly accessible from one side. This openly accessible side or surface is essentially formed by a fuel cell electrode. Sealing material is arranged layer-by-layer above the other opening. At least one portion of the edge of the fuel cell disposed in the opening is covered by the sealing material.