FIELD: process engineering. SUBSTANCE: invention relates to pipe rolling and may be used in pipe cold rolling at roll stands. Proposed mandrel comprises stem and working section with cross section decreasing from said stem generating variable-taper curve, the taper at the end of squeezing section being equal to that of gage development. Mandrel working section features generatrix taper K0 matching that of gage tape in compliance with inequality KT<K0<Kp(1+2f), where f is pipe wall thickening in reduction zone vs diametre reduction in said zone; Kt is mandrel tape at the end of squeezing section equal to that of gage development in that zone, and Kp is gage development taper at the start of working section. EFFECT: higher quality of pipe inner surface, ruling out of fold formation thereon and rejects, reduced metal consumption.