Method and machine for grafting multiplication and propagation parts of grapevines and similar plant varieties, comprising a manual loading step, i.e. a step in which the elements to be grafted are loaded manually, a heeling step and a milling step in which the elements to be grafted are cut, a grafting step in which the cut elements are inserted into each other, and a step in which the thus completed graft is unloaded. The loading step and the heeling step are carried out in two mutually opposing and axially aligned stations, whereas the cutting step is carried out in a sequence by having the elements to be grafted (12, 13) displaced with the help of moving means capable of moving on a horizontal plane.
