The dual interlocking circular cutter (DICC) cutting method, used to produce straight bevel gears (SBGs), employs two interlocked cutters to generate tooth surfaces with a combination of profile and lengthwise crowning. The gear pairs produced have the advantage of low assembly sensibility. However, the cutting method can only be carried out on a dedicated machine with complicated mechanisms, which are not only difficult to setup but also reduce stiffness and accuracy. Gleason recently applied this cutting method on the modern CNC bevel gear-cutting machine to increase productivity and accuracy in manufacturing SBGs; however, they revealed no details of this application because of commercial considerations. The main goal of this work, therefore, is to establish a mathematical model of an SBG produced by the DICC method on a virtual machine. The work gear is cut by an imaginary generating gear that enables derivation of the SBG tooth surface. Ease-off and tooth contact analysis (TCA) are applied to confirm the correctness of the proposed model. A cutting method is also proposed that can be transformed from a specific traditional machine to a modern CNC bevel gear-cutting machine. Conversion from the virtual machine enables derivation of the five-axis nonlinear machine coordinates and subsequent programming of the NC data. Finally, the correctness of NC data for machining is confirmed using the vericut nc verification software.