Abstract: A hemodialyzer in which a sealant anchors the edges of a plurality of generally planar semipermeable membranes to a generally rigid case. The moisture content of the membranes is maintained at approximately a constant value so as to prevent stress from being built up in the hemodialyzer due to changes in the dimensions of the anchored membranes with changes in moisture content. A stack of semipermeable membrane material is confined between wedge blocks within the hemodialyzer case. The wedge blocks permit the hemodialyzer to be assembled without placing shearing stresses on the membrane. Also, by trapping the last pleats of the membrane between the case and the outer surfaces of the wedge blocks the last pleats are easily encapsulated with sealant and thus sealed.