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Oxide membrane of less than 1 μm thickness are formed on the outer surface of a cladding tube by means of an anodic oxidation method. Thus, anodized membranes have greater density and toughness compared with those of oxide layers formed in high temperature water and act as protection membranes against corrosion. Further, when the anodized membranes are annealed in vacuum at 250 to 450degC, cubic oxide membranes are also stabilized in addition to ordinary monoclinic oxide membranes, to form specific oxide membranes in which cubic and monoclinic crystals are present together. Accordingly, this can provide a more excellent corrosion resistance against nodular corrosion compared with conventional cladding tubes. Further, since the improvement of the corrosion resistance is derived from the formation of strong oxide membranes, neutron economy and mechanical properties of the cladding tubes are not degraded as in usual cases. (T.M.)