A method of repairing a vessel bottom head penetration of a nuclear reactor is presented, said penetration comprising a tube fastened to the internal wall of the vessel bottom head by an internal weld bead and emerging outside the vessel bottom head, forming a groove. The method consists inter alia in preparing a mock-up representative of the vessel bottom head penetration to be repaired and in depositing this mock-up on site in an irradiation-free zone, in fastening two half-inserts to this mock-up in the groove, each half-insert having a profile corresponding to the half-profile of the groove, in forming, again on this mock-up, automatically and by remote control, a weld bead in the groove, in carrying out a dimensional check and, after validation of this weld bead, in carrying out the steps of fastening the two half-inserts and forming a weld bead automatically, directly in the groove of the vessel bottom head penetration to be repaired.