In a method and device for machining material, an unfocused beam of laser radiation is focused and directed at the material surface, creating an interface of laser radiation and material to be machined. The beam waist, which results from the focusing the laser radiation, is held in the region of the interface of laser radiation and material. The spacing of the beam waist from the upper or lower side of the interface in the axial direction corresponds at most to triple the value of the penetration depth of the interface into the material. The focusing is effected such that components of the laser radiation are made divergent not just in the propagation direction downstream of the beam waist but also in the beam waist itself and/or also in the propagation direction upstream of the beam waist.