Abstract: In the method and the machine for manufacturing a bundle (33) of thread-like elements such as tubes or electric cables of finite length and including at least one junction point for a branch, and in which the elements of the bundle are covered by a tape (31) of thermofusible insulating material wrapped transversely about the bundle with the longitudinal edges (31a, 31b) of the tape being united by welding, two rows each comprising a plurality of wheels (9 to 14) for driving the bundle (33) and the tape (31) are provided, the wheels pressing against the tape, a V-shape being previously imparted to the tape by a guide situated upstream from the wheels, said rows of wheels defining between them a through path (18) for the bundle, the path being upwardly open and passing successively beneath a first horizontal guide (23) for folding down one of the sides of the V-shape against the bundle, beneath a nozzle (36) for blowing hot air into the angle formed between the folded-down side (31a) and the non-folded-down sid