Recently 5-axis NC machines are widely used in Korea. Since 5-axis machines have two more degrees of freedom than 3-axis machines, it is very important to find desirable tool positions(locations and orientations) in order to make an efficient use of expensive 5-axis NC machines. In this research an algorithm to determine “optimal” tool positions for 5-axis machining of sculptured surfaces is developed. For given CC(Cutter Contact) points, this algorithm determines the cutter axis vectors which minimize cusp heights and satisfy constraints. To solve the optimal problem, we deal with following major issues: (1) an approximation method of a cusp height as a measure of optimality (2) Identifying some properties of the optimal problem (3) a search method for the optimal points using the properties. By using a polyhedral model as a machining surface, this algorithm applies to sculptured surfaces covering: overhanged surface.