The present invention relates to a fibre-application method and a machine intended for the production of parts made from composite material, in particular for applying a fiber web onto convex and/or ridged surfaces. The machine includes a fiber application head and a system (5) for moving said application head. The application head includes a compacting system comprising a compacting roller (2) intended to come into contact with the application surface (90) so as to apply the web and a compacting member (3, 103, 203) placed downstream from said compacting roller and having a substantially planar contact surface (32), whereby the contact surface of the compacting member can be applied against an application surface over substantially the entire width of a web along at least one contact line.