Edge chipping is one of the most serious issues during machining process of brittle materials. To find an effective method to reduce edge chipping, the relationship between the distribution of maximum principal stress and edge chipping is studied comprehensively based on 3D finite element analysis (FEA) model of in-process workpiece structure in this paper. Three-level influencing factors of edge chipping are proposed, which are helpful to understand the relationship between intuitive machining parameters and edge chipping at different levels. Based on the analysis, several experiments are designed and conducted for drilling and slotting to study the strategy of controlling edge chipping. Two methods are adopted: (a) adding additional support, (b) improving tool path. The result show that edge chipping can be reduced effectively by optimizing the distribution of the maximum principal stress during the machining process. Further, adding addtitional support method is extended to more complex parts and also obtain a good result. Finally, how to use adding additional support method, especially for complex parts, will be discussed in detail. Several open questions are raised for future research.