We implement and test a multi-point machining tool positioning technique that positions the tool using only a variation on gouge checking. The result is a method that is roughly twice as fast as an earlier method that performed a numerical search to find a tool position with multiple points of contact with the design surface. A GPU implementation provides an additional factor of ten speedup. Verification of the method was done via simulation and machining and measuring physical parts. Keywords 5-axis machining • Multi-point machining • Gouge checking 1 Introduction Two types of machines, 3-axis and 5-axis machines, are commonly used in manufacturing industries. 5-axis machining have additional degrees of freedom in rotation and tilting about the z-and x-axes, giving extra flexibility in machine kinematics