In the context of a method for the separating machining of plate-like work-pieces from an elastically deformable material, in particular for the separating machining of sheet metal, two workpiece parts are separated from one another, in that the two workpiece parts are initially partially separated from one another, so as to produce at least one connecting web connecting the two workpiece parts to one another, and in that the two workpiece parts are then separated from one another completely by re-moving the connection created by the connecting web. The at least one connecting web is created as a flexure bearing in this case that connects the two workpiece parts to one another in such a manner that the two workpiece parts are movable relative to one another with elastic deformation of the connecting web against the action of a restoring force.