Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets G 1 (tangent-plane) continuity of the neighboring strips along shared boundaries. While for some geometries one cannot achieve G 1 continuity and high approximation quality at the same time, our optimization framework offers a good trade-off between machining accuracy in terms of distance error and the G 1 connection of neighboring strips. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that we are able to meet fine industrial tolerances and simultaneously significantly reduce the kink angle of adjacent strips, and consequently to improve the surface finish in terms of smoothness.