A process of producing an austenitic stainless steel tube comprises the steps of: a) producing an ingot or a continuous casted billet of the austenitic stainless steel, b) hot extruding the ingot or the billet obtained from step a) into a tube, c) cold rolling the tube obtained from step b) to a final dimension thereof. The outer diameter D of the cold rolled tube is 70-250 mm and the thickness t thereof is 6-25 mm, and the cold rolling step is performed such that the following formula is satisfied: (2.5×Rc+1.85×Rh−17.7×Q)=(Rp0.2target+49.3−1073×C−21Cr−7.17×Mo−833.3×N)±Z  (1) wherein Rp0.2target is targeted yield strength and is 750≤Rp0.2target≤1000 MPa, 30≤Rc≤75%, 50%≤Rh≤90%, 1≤Q≤3.6, and Z is 65.