Abstract: The invention relates to an apparatus with hollow fibres, comprising: an elongate enclosure (41) at both ends of which there is a partition (48) supporting the open ends of a bundle of hollow fibres (47), the enclosure (41) being closed at each of its ends by a cover (50).This apparatus is characterized in that it comprises a circular resin-based seal (55) arranged on the periphery of the partition (48) and in the proximity of the hollow fibres (47), this seal (55) forming to the inside of the enclosure a concave connecting surface (56) joining without substantial break of continuity the inner surface (52) of the cover (50) to the partition (48) or to the end surface (49) of the enclosure.This apparatus can be used in particular as an artificial kidney.