A machine for machining, such as cutting and/or forming, planar workpieces has an upper tool and a lower tool that are movable toward each other to machine a workpiece arranged therebetween. The upper tool includes at least one cutting tool having at least one cutting edge and a clamping shaft. The lower tool includes a main body having a support surface for the workpiece. The support surface has an opening associated with an inner counter cutting edge. The lower tool has a positioning axis and at least one outer counter cutting edge provided outside of the opening and associated with the support surface. The outer counter cutting edge is aligned with an outer face of the support surface. A distance of the outer counter cutting edge from the position axis and a distance of the inner counter cutting edge from the position axis deviate from each other.