In this paper, we study tool design problems encountered in using a punch press Flexible Manufacturing System (FMS) for producing flat sheet-metal parts. We consider the problem of designing the minimum number of tools needed to punch a given set of holes in the parts. Holes described by a single attribute as well as two attributes are considered. We model the tool design problems as graph theoretic problems. Such an approach is believed to be new for the problem studied. We have made the following major contributions: First, we show that the two-attribute tool design problem is equivalent to the minimum clique cover problem on the intersection graph of rectangles, which is a well known NP-complete problem. Second, we develop a fast algorithm to construct a set-covering formulation from the underlying graph model. In addition, we show that our approach has applications beyond the tool design problem (e.g., location problems).