In a method and apparatus for continuously supplying slivers mechanically to a roving frame, wherein a plurality of aligned sliver cans are arranged along the longitudinal direction of the roving frames in a taper arrangement with regard to the volume of sliver contained therein, full packaged sliver cans are aligned at a standby position adjacent to and facing the aligned sliver cans which contain the smallest volume of sliver therein, and when the above-mentioned sliver cans having the smallest volume of sliver reach an almost exhausted condition, a unit sliver piecing operation of piecing a free end of sliver from one of each of the full packaged sliver cans with a free end of each sliver supplied to the roving frame, created by separating same from each sliver supplying can facing thereto, is carried out in steps at all of the above-mentioned full packaged sliver cans, and when the full packaged sliver cans are at the standby positions thereof, a position of an end of a sliver from each of the full packaged sliver cans is regulated to a predetermined angular position with respect to the longitudinal axis of the sliver can.