An electrical energy storage cell is provided with: an active part which is equipped and adapted to store electrical energy supplied from the outside and to discharge stored electrical energy to the outside; at least two current conductors which are connected to the active part and are equipped and adapted to supply electric current from the outside to the active part and to discharge electric current from the active part to the outside; and an enclosure, which defines a prismatic basic shape having a substantially cuboid-like outline and encloses the active part in a gas-tight and fluid-tight manner. According to the invention, the enclosure has two flat foil parts and a peripheral seam part connecting the edges of the foil parts, wherein the seam part surrounds the active part in the manner of the frame and has sections of maximum thickness, in which the thickness is uniformly greater than the thickness of the active part. A cell block comprises a plurality of said electrical energy storage cells, wherein the cells are stacked in the direction of the thickness thereof and, together with connecting terminals, form an electrical energy storage device which can advantageously be used in a vehicle.