The invention provides a flattening method for flattening the edges of a swatch of flexible material from which pieces are to be cut out. The method comprises: establishing a digital representation of at least a portion of an outline (HC) of the swatch of flexible material (H); establishing a specific flattening direction (Di, Dj) and distance (Vi, Vj) for each of the points (Pi, Pj) of the scanned portion of the outline of the swatch; and for each selected point of the scanned portion of the outline of the swatch, using a presser foot of a cutter tool, to flatten the edges of the swatch along the specific flattening direction and distance established for said point, and along a flattening direction going from within the swatch towards its edges.