Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects 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, and to generate NC tool path in CAD/CAM system.