Abstract: A flatbed die-cutting press (10) for cutting detailed shapes in sheets (20) of foldable paper or board material that are typically fed at a rate of 6000 to 14000 sheets/hour, comprises a cutting tool assembly (40) having an apertured female die part (42) with a series of apertures (44) defining typically a complex shape or shapes to be cut out. The female die part (42) is associated with a suction channel (46) arranged so that parts (22) that are cut out of the sheets (20) are removable by suction through the apertures (44). This enables the cutting of small shapes and complex shapes whose outline extends over an area of at least several square centimeters that contains a group of cut-outs comprising a plurality of straight or curved lines or strokes all having a section less than 2 mm, possibly less than 1 mm, along all or a substantial part of their length, for the mass production of blanks of paper or board material particularly cigarette packages, where the cut-outs form an emblem on the package.