To provide a method for producing a seamless steel tube excellent in internal pressure fatigue by suppressing wrinkle flaws generated at the inner surface of a steel tube rolled by a Mannesmann-mandrel mill tube making process.

When a seamless steel tube is subjected to hot working by a Mannesmann tube making process, it is subjected to Mannesmann perforation rolling and Mandrel extension rolling, thereafter, a reheating condition is controlled to 800 to 1,050C, and, in accordance with the finish dimensions t/D in fixed diameter rolling by a stretch reducer, under the condition where the average ellipse rate Y of a caliber roll satisfies equation (1), finish rolling is performed; wherein, in equation (1), Ln is a natural logarithm, and, regarding in equation (2), i=1 to N, and a caliber major axis Ai(mm) and a caliber minor axis Bi(mm) are denoted: Y(%)-2.56Ln(t/D100)+10.29 (1), and Y(%)=((Ai-Bi)/Ai100)/N (2). Preferably, the hot-finished steel tube is further subjected to cold drawing at a thickness working degree of 10%.