A battery module has a plurality of round cells of identical dimensions, nominal charge capacity and voltage. They are grouped into a series of round cell stacks which are arranged one behind the other in a row and which all consist of an identical plurality of round cells which lie in each round cell stack axis-parallel to the stack row direction, adjacent and atop each other, in identical position in the stack row direction. There are contact plates arranged between adjacent round cell stacks, which electrically connect the round cells of each round cell stack in parallel to the poles thereof situated in the stack row direction. All round cells are arranged in such a way that all identical electrical poles face in the same direction and form a plurality of aligned round cell rows. The contact plates have protrusions of identical dimensions, each contacting a pole of a round cell but which are not integrally connected to the pole, such that all round cell poles are contacted via one of the protrusions. The contact plates are electrically conductive on the protrusions and in flat sections between the protrusions. A pole plate contacts the end-side contact plate on each of the two ends of the round cell stack row, and said pole plates are thicker-walled relative to the contact plates.