A method of laying up a segment on a layup surface using a layup head that is mobile with respect to the layup surface, the layup head supporting a spool of a tape of material which includes at least one layer to be laid up from which said segment is cut and at least one interliner, the method including applying the tape of material against the layup surface and removing the interliner using a separator. The tape of material is pressed firmly by a press roller against the layup surface before the interliner is removed as the layup head moves in an advancing movement. A layup head for implementing the method and a layup machine including the layup head are also described.