Abstract: The cutting device includes a blade (1), in which either the blade (1) can move relative to a sheet of flexible material (4) or the sheet of flexible material (4) can move relative to said blade (1), and the blade (1) is associated with a plurality of independent flexible bristles (2), which press and stabilize the flexible material vertically and/or horizontally against a base (5) where the flexible material to be cut is supported. The device can be used to apply constant and well-distributed pressure on the flexible material in the cutting zone, preventing the material from wrinkling and securing the same in an optimal manner relative to the blade, thereby facilitating the cutting.