Abstract: Physics and geometry based variational techniques for surface construction have been shown its remarkable superiority on designing high quality surfaces.We derive an Euler-Lagrange equation from the geometric invariant curvature integral functional which was proposed by Greiner.Using this Euler-Lagrange equation,we construct a sixth-order geometric flow,which is solved numerically by a divided-difference-like method.The proposed equation is applied to solve several surface modeling problems,including surface blending,N-sided hole filling and surface recovery.The illustrative examples show that this flow yields high quality surfaces.