In a fuel cell assembly comprising a plurality of cell each including an electrolyte layer (2), a pair of diffusion electrode layers (3, 4) interposing the electrolyte layer between them, and a pair of flow distribution plates (5) for defining passages (11) for fuel and oxidant fluids that contact the diffusion electrode layers, the fuel cells are arranged on a common plane. Therefore, the vertical dimension of the fuel cell assembly can be minimized, and a fuel cell assembly of favorable electric properties can be achieved. Each flow distribution plate is typically formed with communication passages for communicating fluid passages defined on each side of the electrolyte layer at a prescribed pattern. The communication passages and through holes communicate the fluid passages in such a manner that adjacent fuels cells have opposite polarities.