An apparatus for continuously manufacturing a corrugated sheet having a varying fold width and also having fold lines extending either straight or in wavy or zig-zag fashion in a direction widthwise thereof. The apparatus includes upper and lower toothed rolls each made up of a group of toothed discs and having a circumferential groove defined between each neighboring toothed discs. At least one of the upper and lower toothed rolls is supported for adjustment in position relative to and in a direction towards and away from the other of the upper and lower toothed rolls. Upper and lower guide bars while extending in a direction parallel to the upper and lower toothed rolls are accommodated within the circumferential grooves for movement in a direction towards and away from each other over a distance corresponding to the height of each tooth of any one of the upper and lower toothed rolls. During a continuous passage of the web of sheet through a biting region defined between the upper and lower toothed rolls, the web of sheet is alternately folded by the interaction between the upper and lower toothed rolls to provide the corrugated sheet.