Abstract: A metal workpiece is rolled in a rolling mill, including an upstream rolling stand or pinch rolls and more than one stream rolling stand. The roll gaps of the workrolls of the downstream rolling stand are set so that the eqivalent contact angle .theta.e (.theta.e=tan.sup.-1 (cos .alpha..times.tan .theta.) wherein .theta. denotes the contact angle between the workrolls in the bottom of the roll groove and the workpiece and .alpha. denotes the inclined angle of the groove) is larger than tan.sup.-1 .mu. (.mu. denotes a coefficient of friction between the workpiece and the workrolls at the time of biting therebetween and also is smaller than tan.sup.-1 .mu.' (.mu.' denotes a coefficient of friction between the workpiece and the workrolls when the workpiece is completely bitten between the workrolls and the rolling operation is in progress).

Abstract: In the rolling of metal material to round cross-sectional shape through a succession of three roll stands with the horizontal-horizontal-vertical, or vertical-vertical-horizontal rolls arranged in this order in the rolling down direction for achievement of increased accuracy of dimensional control at finish, an initial metal stock of specific oval cross-section is rolled to an intermediate and small reduction through the first and second stands forming specific oval groove, and then to a finish and small reduction through the third stand forming a round groove.