A method for production of a fuel cladding tube for a nuclear reactor, characterized by the preparation of an ingot of an alloy of zirconium with the following composition by weight %: 0.8%.ltoreq.Nb.ltoreq.2.8%, traces.ltoreq.Sn.ltoreq.0.65%, 0.015%.ltoreq.Fe.ltoreq.0.40%, C.ltoreq.100 ppm, 600 ppm.ltoreq.O.ltoreq.2300 ppm, 5 ppm.ltoreq.S.ltoreq.100 ppm, Cr+V.ltoreq.0.25%, Hf.ltoreq.75 ppm and F.ltoreq.1 ppm the remainder being zirconium and impurities arising from production. The ingot is then subjected to forging, a hardening and thermomoechanical treatments comprising cold laminations separated by intermediate annealing, all intermediate annealings being carried out at a temperature below the .alpha..fwdarw..alpha.+.beta. transition temperature of the alloy, finishing with a recrystallization annealing and resulting in the production of a tube, whereupon an optional external cleaning of the tube is carried out and a mechanical polishing of the external surface of the tube is carried out to give a roughness Ra less than or equal to 0.5 .mu.m. The invention further relates to a fuel cladding tube obtained thereby.