To use a steel tube cold worked as it is by controlling a final finish working rate as taking a ratio of a working rate between tube thickness and outer diameter for a parameter when producing a two phase or austenitic stainless steel tube used for a deep gas well/oil well under severe corrosive environment so as to improve a compression strength ratio against tensile strength in the axial direction.
A working rate of a thickness is set to Rr% and a working rate of an outer diameter Rb in a final process, cold working is conducted so that a working parameter Q value obtained by the following equation is set to ≤1.5. Q=Rr/Rb here Rr=(To-T)/To Rb=(Do-D)/Do but To: tube thickness before working mm T: tube thickness after working mm Do: outer diameter before working mm D: outer diameter after working mm By this method, a steel tube, in which compression strength in the axial direction is ≥80% of tensile strength, is surely produced. Further, a cold steel tube stock may be either of hot or welded tube.