A battery cell housing includes a housing shell and a housing cover. A bearing surface and a first connecting surface separate thereto are present on the housing shell (16) on at least two mutually facing side walls or on all side. A contact surface on the housing cover is associated with each bearing surface and a second connecting surface on the housing cover is associated with the first connecting surface. The relative position of the second connecting surface and of the contact surface is adapted to the relative position of the bearing surface and of the first connecting surface. The contact surface and the second connecting surface can thus be spaced apart in the vertical direction (H) and/or the second connecting surface is present on an edge side strip extending downwards in the vertical direction (H) to a bottom of the housing shell.