A battery module incorporates features of both prismatic housings and metal foil laminate pouch housings, and is configured to receive and support electrochemical cells. The battery module housing includes a rigid tubular frame and flexible cover elements that are joined to the frame and close the open ends of the frame. The frame has an inner surface that faces the cells, an outer surface that is opposed to the inner surface, a first edge that joins the inner surface to the outer surface at one open end of the frame, and a second edge that joins the inner surface to the outer surface at the opposed open end of the frame. The first cover element overlies and closes the one open end of the frame and the second cover element overlies and closes the other open end of the frame.