The invention concerns a machine comprising driving means (14, 16, 18) for driving sheets in a drive direction (F) through a processing zone (T), and processing means including a tool (53, 53′) and a counter tool (56), respectively, borne by a first and by a second transverse rotary support shaft (52, 54). Said processing means are designed to produce in the sheets cutouts and folds transverse to their drive direction. The counter tool has a substantially cylindrical surface having at least one working strip (57) which extends parallel to the axis of the second support shaft and is radially offset relative to the portions (58) of said surface which are adjacent to said strip, the latter being designed to cooperate with the tool to form a cutout or a fold in a sheet.