An austenitic alloy tube subjected to a cold working and an annealing heat treatment contains C: 0.01% to 0.15%, Cr: 10.0% to 40.0%, Ni: 8.0% to 80.0%, in mass %, and has a metallographic structure satisfying the following Expressions (i) to (iii). R≦f1  (i) R=I220/I111  (ii) f1=0.28×(F1118.0/(F1118.0+0.358.0))  (iii) Where, in the above Expressions, R is a ratio of an integrated intensity of {220} to an integrated intensity of {111} on a surface layer which is measured by a grazing incidence X-ray diffraction method, I220 is the integrated intensity of {220}, I111 is the integrated intensity of {111}, and F111 is full width of half maximum of {111} on the surface layer which is measured by the grazing incidence X-ray diffraction method.