The invention relates to an object (1) that is cut by means of a laser and a water beam and to further processing of the cut material. The object is glued on a carrier (3) that is provided with an adhesive and can be transparent for the radiation used in the water beam (7). The carrier can be a solid body and preferably a fibrous mat (3). Said body or mat is penetrated by the water beam. The object (1) or the cut material thereof is held on the carrier (3) before, during and after cutting through in such a way that said object or material does not change position. In a preferred embodiment, a silicon wafer is used as the object because of the high cutting exactness to be obtained. Other materials can also be used.