Abstract: To expand the suitable conditions of the present blending methods,the problem of blending three quadratic algebraic surfaces along planar sections was transformed into a problem of ascertaining the existence of nonzero solution of homogeneous linear equations corresponding to these three quadratic algebraic surfaces under the condition without considering the existence of quadratic control surfaces.The existence conditions of cubic and quartic blending surfaces were given,i.e.,the ranks of the coefficient matrixes of their linear equations are less than 24 and 60 respectively,and the unconditioned existence of quintic blending surfaces was proved.Finally,the corresponding blending algorithm was presented.