Abstract: A treating period T=L.sub.0 /V is determined from a preset treating length L.sub.0 and a stock running speed V. An advancing acceleration is made as small as possible consistent with a requirement that an advancing time T.sub.F of the treating machine (=advancing positioning interval t.sub.1 +settling time t.sub.s +treating interval t.sub.c +retracting deceleration interval t.sub.2) is equal to or less than T/2 and a requirement that (t.sub.1 /2+t.sub.s) V assumes a given value. Both a retracting acceleration and a retracting speed are made as small as possible consistent with a requirement that an advanced distance is equal to a retracted distance and a requirement that a stop positioning interval t.sub.6 is made as close to a minimum value as possible.

Abstract: A sheet stock feed line in which sheet stock is leveled and fed by a leveler to a feeder and each time the feeder feeds the sheet stock by a predetermined length, the feed by the feeder is stopped for working the sheet stock. While the feed by the feeder is stopped, the leveler feeds the sheet stock at a very low feed rate to form a loop of the sheet stock between the leveler and the feeder. When the loops reaches a predetermined size, the feeder resumes the feed of the sheet stock and the leveler is controlled so that its feed amount follows that by the feeder.