Although face milling is a popular industrial cutting method for mass-producing bevel gears, current machines require many cutters with diverse profile angles to produce different gear types. In this paper, therefore, a flexible cutting method is proposed that eliminated the need of too many cutters for producing the gears with similar size and module by employing cutters with standard profile angle blades on a general five-axis machine. The settings for this machine are derived by mathematically modeling a virtual machine, after which the motion functions of the five-axis coordinates are determined through inverse kinematics. A sensitivity analysis is then performed to bring the tooth surface produced closer to its theoretical counterpart. The results of a cutting simulation confirm the correctness of this proposed method.