The application of wire EDM to the machining of cylindrical parts is an emerging research topic. The current research is mainly focused on the machining of micro-cylindrical parts, and there is little research on the general-sized parts. This paper proposes to apply the principle of contour approximation method to the machining of cylindrical parts of general size. First, the basic principle of the contour approximation method is introduced, and the machining process is divided into three parts: roughing, semi-finishing and finishing. Roughing corresponds to polygon cutting. Second, the various indicators of polygon cutting are analyzed. The influence of the number of polygonal sides on the residual height and residual area is analyzed. Two methods are proposed for polygon cutting: sequential cutting and multiple edge cutting. The calculation formulas for the processing volume of the two methods are deduced. By comparing the two methods, it is found that different methods are applicable to different part sizes. At last, machining experiments were carried out. The selection of residual variables and the determination of polygon machining methods are detailed. The process parameters and machining time of each stage are listed. In addition, the measurement results of each stage of the machining are also analyzed.