Hermite method and MPM method were studied. Multi-point machining constraints with the cutter tilting forward and backward were derived respectively. So the number of the solutions of the two Multi-point machining methods was doubled than before. To derive some general conclusions about solution areas of Multi-point machining constraints, structure of neighborhood region close to a given point on a surface was used to substitute the surface in the Multi-point machining error calculation. A computational example was also given in the paper. With the theoretical analyses and computational example, it was proved that, for an open and slightly curved surface machining with Multi-points method, without regard to interference, there were four branch areas satisfying Multi-point machining constraints and distributing radically nearby the first tangent contact points respectively on condition that the cutter was tilted forward or backward. And they extended basically in the directions along the principal curvatures at the first tangent contact point.