Abstract: To process with free-form deformation,a Bézier surface is embedded into a tetrahedron.The new surface is the composition of a tensor product Bézier surface and a tetrahedral Bézier volume.The composted surface is a Bézier surface whose control points can be got using shifting operators and de Casteljau algorithm.Finally,the formula to calculate the order2and3free-form deformation of the rectangle mesh are given.