Abstract: In this paper, we prove that given two cylinders whose axes are non-coplanar, in general, there doesn't exist a cubic GC^{1 blending surface for any clipping planes. We introduce a new trick, i.e., to constructing an auxiliary cylinder whose axis is coplanar with each of the two axes of the two given cylinder respectively and then obtain the two-piece cubic GC1 blending surfaces by using Wu Wen-tsun Formulae of t wo coplanar cylinders.}

Key words: non-coplanar tubes, WU Wen-tsun formulae, blending surfaces