In a device for material processing by laser radiation, including a source of laser radiation emitting pulsed laser radiation for interaction with the material; optics focusing the pulsed processing laser radiation to a center of interaction in the material and a scanning unit shifting the positions of the center of interaction within the material. Each processing laser pulse interacts with the material in a zone surrounding the center of interaction assigned to the laser pulse so that material is separated in the zones of interaction. A control unit controls the scanning unit and the source of laser radiation such that a cut surface is produced in the material by sequential arrangement of zones of interaction. The control unit controls the source of laser radiation and the scanning unit such that adjacent centers of interaction are located at a spatial distance a ≦10 μm from each other.