A solid electrolyte fuel cell plate structure includes a cell element layer composed of a solid electrolyte, an air electrode layer and a fuel electrode layer, a porous base body supporting the cell element layer, and a gas-impermeable member having electric conductivity. The cell element layer is arranged such that the solid electrolyte layer is sandwiched between the air electrode layer and the fuel electrode layer, with the air electrode layer or the fuel electrode layer being joined to the porous base body. The gas-impermeable member is associated with the solid electrolyte layer to allow gas internally passing through the porous base body to be separated from gas flowing outside the porous base body. Such a cell plate structure can be employed in a solid electrolyte fuel cell stack, which in turn can be employed in a solid electrolyte fuel cell electric power generation unit.