Abstract A new tool path generation method of flank milling considering constraints is proposed for ball-end cutters in this paper. It will not only reduce the machining error range but also meet the following two constraints: (a) The ball end of the milling tool is tangential to the constraint surface; (b) There is no overcut and the minimum error is zero, which is called nonnegative-error constraint. The two constraints are very useful in some situations of engineering applications, such as flank milling impeller blades. Based on the proposed method, two types of cutter will be used to generate tool paths for the same designed surface and constraint surface. The effectiveness and accuracy of the proposed method will be finally proved with some examples.