Abstract: A knife support is part of the apparatus, and with a knife it passes by at the edge of the work piece which is to be deburred. The edge of the knife corresponds in its length at least to the length of the edge to be deburred. In order to be able to shear both the front end and the rear end of slabs with one and the same construction in a simple and sturdy way, the knife support is provided as a rocker arm which can be moved with a pivot drive. The swivel axis of the rocker arm can be directed about parallel to the edge of the work piece to be deburred.