The optimization problem involving straight turning operations for bar components with constant finished diameters has received extensive attention. In the real-world turning processes on a computer numerical control (CNC) machine, the cylindrical stocks are frequently machined into their desired continuous profiles. Such turning processes require not only straight turning but also face turning, taper turning and circular turning to complete the removal of stock. However, machining models proposed in the literature do not simultaneously consider these turning operations to optimize machining conditions (parameters). This study formulates a machining model to optimize the machining conditions for turning cylindrical stocks into continuous finished profiles, thereby extending the applications of machining optimization. The usefulness of the developed machining model is finally established through a test example.