Curvature catering is a high-efficiency method for machining sculptured surfaces using 5-axis machine tools. By means of this method, the condition of interference in the vicinity of the contact point is critical, cannot be detected using the methods based on curvatures at the point. This paper presents the algorithms for detecting the interference due to the rim, front cutting edge and opposite side of a disc-type milling cutter, and the methods for eliminating these kinds of gouge. Since toolsize interference can be detected in the process of calculating tool position and axis, is not involved in this paper. The interference due to the outer cone and tool axis will rarely occur during machining open surfaces, nor is discussed at this stage.