A process for the repair by lining of a tube (12) of a steam generator, and a lining for such repair. The lining (15) is introduced into the tube (12), is rolled in the tube (12) inside the tube plate (11) and radially expanded through rolling of its end part (18) located in the tube (12) outside the tube plate (11). Leak-proofing is ensured by brazing the end part (18) of the lining in the tube (12). In its end zone (18), the lining (15) has slots filled with brazing metal and grooves coaxial with the lining (15), which make it easier for the brazing metal to spread. The invention applies particularly to the steam generators of pressurized water nuclear reactors.