Abstract: Dialysis apparatus is provided of the type comprising a casing housing a central cylindrical core which is surrounded by a plurality of layers of capillary tubes constituted by hollow, semi-permeable, fibres. Blood to be treated is caused to flow through the capillary tubes while dialysing solution is passed over the outer surfaces of the tubes. To facilitate the construction of dialysis apparatus with different dialysing surface areas without altering the dimensions of the casing or core, the core is arranged to dismountably carry a plurality of spacing annuli around which the layers of capillary tubes are wound. The diameter of the annuli determines how many layers of capillary tubes can be accommodated in the casing.