This paper presents an algorithm to obtain the intersections of a free-form surface with a series of parallel planes. When sectioning the surface with parallel planes, the change of the topology of the intersection curves is caused by characteristic points of the surface. There are seven types of characteristic points: interior maximum, interior minimum, interior saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersections are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, to generate NC tool path for surfaces, and to generate slices for rapid prototyping.