Semipermeable membranes (2) are arranged in a stack separated by supporting plates (1) having a first plane face and a second plane face (10,12) and comprising through-openings (7,8) connected to an inlet and outlet, respectively, for a first fluid, by means of which this first fluid is conducted to the one side of the respective membrane, whilst a second fluid is conducted ot the other side of the membrane, the stack of membranes and supporting plates having an elongated shape with a flow-through duct formed of the said through-openings (7,8) arranged straight through the stack near its two ends. The invention is characterized by channels (11,11′) originating from end edges (9,9′) of the supporting plates, open towards a frist plane face (10,12), for the conducting of the said second fluid past a seal (13,13a′) arranged on the opposite plane face (12,10) to an opening (14,14′) passing through the plate for the conducting of this second fluid to, respectively from, the space inside the said seal (13,13a′) on the said opposite plane face (12,10) of the plate. The arrangement in accordance with the invention is intended in particular to be used in connection with dialysis, haemofiltration and similar extracorporeal procedures for the treatment of blood.