For material processing of a material, which is in particular for a laser beam to a large extent transparent, asymmetric shaped modifications are created transverse to the propagation direction of the laser beam. Thereby, the laser beam is shaped for forming an elongated focus zone in the material, wherein the focus zone is such that it includes at least one intensity maximum, which is transverse flattened in a flattening direction, or a transverse and/or axial sequence of asymmetric intensity maxima, which are flattened in a sequence direction. After positioning the focus zone in the material, a modification is created and the material and the focus zone are moved relative to each other in the or across to the flattening direction or in the or across to the sequence direction for forming a crack along an induced preferred direction.