PURPOSE: To provide a caliber design for a cold pilger mill which is improved in the quality to give rise to a stress peak value in a tube and efficiency and is enhanced in the life of rolls.

CONSTITUTION: The rolling caliber has an asymmetrical cross-section deviating from a circular shape in at least part of its developing part for rolling. In one embodiment, the respective ring rolls 1, 2 have the cross-sectional contours at which the caliber side edges forward in the rotating direction of the tube R are more strongly curved to a recessed shape than the backward side edges. Namely, the caliber cross-sectional surfaces of the side edges rotated in the transversely flaring portions of the tube so as to arrive at these portions are larger than the caliber cross-sectional surfaces of the side edges rotated in the transversely narrower portions of the tube so as to arrive at these portions.