A fiber application machine including a fiber application head with an application roller for the production of parts made of composite materials. The fiber application head further includes a guiding system to guide the fibers onto the application roller and/or means for the application of resin to each fiber as the fibers leave the guiding system. The fiber application machine can also include a fiber storing system and conveying means for conveying the fibers from the fiber storing system to the application head. The conveying means can comprise flexible tubes, each tube being able to receive a fiber in its inner channel. The conveying means can further include a tension limiting system positioned between the application head and the storing system. The fiber application machine can further include a system for moving the application head.