The present disclosure is directed at a cell carrier, a stack that includes multiple cell carriers, and a method for assembling the stack. The cell carrier has a rigid backing and bus bar supports that are rigidly mounted to the rigid backing The bus bar supports have sockets positioned to receive fasteners for securing bus bars to the bus bar supports. A battery cell that has electrodes in the form of pliable tabs can be secured to the cell carrier by, for example, adhering the cell body to the rigid backing The cell tabs are secured between the bus bars and the bus bar supports when bus bars are fastened to the bus bar supports, and the rigidly mounted supports help prevent relative motion between the cell body and tabs. This helps prevent the cell tabs from ripping or tearing when the battery cell is subjected to vibrations during use.