Cutting system for leather, fabrics and synthetic materials in rolls or sheets by means of oscillating knife, said vibrating blade, mounted on a movable head by means of a bridge arm. The cutting profile is determined from information transmitted by a vector data-file and projected directly onto the work plan for the optimal placement of shapes. Suction and blockage system of the material, head and multi tool system of automatic nesting complement the machine functions. Versions suitable for modeling, small and large productions..