Abstract: A laser engraving machine (4) is used for engraving a workpiece surface (22) by a modulated laser beam in order to form a desired profile in the workpiece surface. The fine structures of the profile are formed by the laser beam of a first laser which is modulated by an acoustooptic modulator (12) with relatively high modulation frequency, while the deep areas of the desired profile are formed by the laser beam of a second laser (10), for which purpose the modulator (12), on the one hand, and the second laser beam source (10), on the other hand, are driven by interrelated but separate control signals (S3, S2). The two perpendicular polarized laser beams from the modulator (12) and the second laser beam source (10) are transmitted and reflected by a selective mirror (14), respectively, and applied commonly via an optical system (18) to the workpiece surface (22) to be machined.