A method of generating n-sided (n=3,5,6) G2 blending surfaces (except that the 3-sided blending surface is C0 continuous at the three vertexes and the 5-sided blending surface is C0continuous at a vertex) is presented in this paper. When this method is used to generate n-sided (n=3,5,6) G2 blending surfaces between the base surfaces, the base surfaces are expressed as n-sided (n=3,5,6) by reparameterising the base surfaces; then the n-sided (n=3,5,6) G2 blending surfaces are convex combinations of the base surfaces expressed as n-sided (n=3,5,6) surfaces. When the contact curves are arbitrary curves in the base surfaces, the regions near the contact curves in the base surfaces are reparameterised and expressed as n-sided (n=3,5,6) surfaces; then the n-sided (n=3,5,6) G2 blending surfaces are convex combinations of the reparameterised local base surfaces expressed as n-sided (n=3,5,6) surface styles. The shape of the n-sided (n=3,5,6) blending surfaces can be adjusted by changing the size of the reparameterised local base surfaces and the combination weights. An example of a 5-sided surface generated between an aerofoil, the body and the fringe surface of a missile is given.