Abstract: The invention relates to a process and an apparatus for the production of a bundle of filaments from at least one filament, and its application especially to the production of a bundle of hollow semi-permeable fibers used for producing a filtration module. According to this invention, the filaments (1) is wound in a first step, in several superposed layers around a support plate (10) having two take-up edges (17) perpendicular to the direction of winding of the filament, and conferring on this filament an alternating transverse movement of decreasing amplitude in such a manner as to achieve a winding having a predetermined profile. The support plate (10) is then removed by retracting the take-up edges (17) toward each other so as to obtain a bundle having a transverse section which is a function of the profile of the winding and curved ends.