A battery module for a motor vehicle includes two contact-making plates, which are arranged in parallel or approximately in parallel with one another, including a first and a second contact-making plate, and a plurality of battery cells, which are arranged next to one another and between the two contact-making plates. Each battery cell has a longitudinal axis and two axially opposite ends. The ends of each battery cell are connected to the contact-making plates, and the battery cells are arranged in such a way that i) an outer circumferential surface of each battery cell fully surrounded by adjacent battery cells touches outer circumferential surfaces of at least three adjacent battery cells, and ii) an outer circumferential surface of each battery cell not fully surrounded by adjacent battery cells touches outer circumferential surfaces of at least two adjacent battery cells.