A process for the manufacture of rotational parts from a three-dimensional material comprising the steps of producing a supporting mandrel provided with longitudinal and circumferential rows of barbs which between them define longitudinal corridors and circumferential corridors, placing superimposed layers of longitudinal threads and of circumferential threads in the said corridors, densifying the assembly thus obtained, then eliminating the supporting mandrel, placing some of the longitudinal threads in only a portion of the length of the corresponding longitudinal corridors, extremities of said some longitudinal threads being temporarily held in position by a first retractable member, said some longitudinal threads being then caused to come back into the corresponding longitudinal corridors over said first retractable member, said extremities being then held in position inwards of the first retractable member by a second retractable member, said first retractable member being then withdrawn in a direction that is substantially tangential with respect to the mandrel, and at least one holding wire being wound on in at least one circumferential corridor next to said extremities, thereby continuously holding said extremities in position.