This thesis presents models and algorithms necessary to simulate the five-axis flank milling of jet-engine impellers in a virtual environment. The impellers are used in the compression stage of the engine and are costly, difficult to machine, and time-consuming to manufacture. To improve the productivity of the flank milling operations, a procedure to predict and optimize the cutting process is proposed. The contributions of the thesis include a novel cutter-workpiece engagement calculation algorithm, a five-axis flank milling cutting mechanics model, two methods of optimizing feed rates for impeller machining tool paths and a new five-axis chatter stability algorithm. A semi-discrete, solid-modeling-based method of obtaining cutter-workpiece engagement (CWE) maps for five-axis flank milling with tapered ball-end mills is developed. It is compared against a benchmark z-buffer CWE calculation method, and is found to generate more accurate maps. A cutting force prediction model for five-axis flank milling is developed. This model is able to incorporate five-axis motion, serrated, variable-pitch, tapered, helical ball-end mills and irregular cutter-workpiece engagement maps. Simulated cutting forces are compared against experimental data collected with a rotating dynamometer. Predicted X and Y forces and cutting torque are found to have a reasonable agreement with the measured values. Two offline methods of optimizing the linear and angular feeds for the five-axis flank milling of impellers are developed. Both offer a systematic means of finding the highest feed possible, while respecting multiple constraints on the process outputs. In the thesis, application of these algorithms is shown to reduce the machining time for an impeller roughing tool path. Finally, a chatter stability algorithm is introduced that can be used to predict the stability of five-axis flank milling operations with general cutter geometry and irregular cutter-workpiece engagement maps. Currently, the new algorithm gives chatter stability predictions suitable for high speed five-axis flank milling. However, for low-speed impeller machining, these predictions are not accurate, due to the process damping that occurs in the physical system. At the time, this effect is difficult to model and is beyond the scope of the thesis.