Five-axis computer numerically controlled (CNC) flank milling is widely used in the manufacturing of complex free-form surfaces, such as turbine blades, impellers, blisks, and spiral bevel gears, due to its high productivity and superior surface quality compared with point-milling approaches. However, conventional flank milling methods mainly rely on cylindrical or conical cutters, which often fail to satisfy the tight geometric tolerances and smoothness requirements demanded in modern industrial applications . Furthermore, existing multi-strip toolpath planning strategies frequently introduce gaps or overlaps between neighboring strips, causing visible machining artifacts and reduced surface quality. This thesis presents a novel optimization-based framework for 5-axis CNC flank milling of free-form surfaces using both straight and custom-shaped tools. The proposed method simultaneously optimizes the tool geometry and the tool motion to improve machining accuracy. Starting from a free-form reference surface and a guiding curve, tangential motions of sphere quadruplets aligned along a straight line are analyzed to construct candidate tool shapes and corresponding motions. These motions are further refined using a global optimization framework that minimizes the approximation error between the tool envelope and the target surface while preserving smooth tool behavior. In addition, a new multi-strip flank milling strategy is introduced to achieve approximate G1 continuity between neighboring strips. The proposed optimization balances machining accuracy and tangent-plane continuity, significantly reducing discontinuities along shared strip boundaries. The developed algorithms are validated on both synthetic free-form surfaces and industrial benchmark datasets, including blisk blades and spiral bevel gears. Experimental and simulation results demonstrate that the proposed approach achieves tight industrial tolerances while substantially improving surface smoothness. Compared with the commercial software Siemens NX, the proposed framework reduces machining errors by more than 85% and improves continuity between neighboring toolpaths.