Procedure and device for cutting pieces of material to order, from a band of material, by using a cutting table equipped with a vacuum installation for holding the band of material in place and a workable, longitudinal and traverse slide on the cutting table, running along the desired cutting lines, which is controlled by a data processor for marking and data control, as the carrier of a cutting tool driven by ultrasound, for the purpose of which a conveyor belt with a base similar to a brush serves as the means of transport for the band of material in the cutting area and as a cutting base, which is moved, step by step, by means of a slide range that, for the finished cut of a piece of material, is larger than the cutting tool's most ample movement in the longitudinal direction (X), for which purpose, the cutting tool in each case is only moved following the transportation phase, with the conveyor belt being stationary all along the cutting lines.