Membrane cell stack arrangement and method of manufacturing such a membrane cell stack arrangement. The arrangement has a housing (2) having a central axis, and a stack of membrane cells (4), each membrane cell (6) being arranged inside the housing (2) with a major surface (6a) of the membrane cell (6) oriented substantially perpendicular to the central axis. Each membrane cell (6) has a corner recess (12) between each two adjacent sides of at least four sides (10a-d). Sealing compartments (14) are provided by corner recesses (12) of adjacent membrane cells of the stack of membrane cells (4) in co-operation with a part of an inner surface (2a) of the housing (2).