Function approximation is one of the most important "elds of research in design optimization. Accurate function approximation reduces the repetitive cost of "nite element analysis. Many local approximations, such as one-and two-point local approximations, are already available. These are, however, only valid in a small domain and require stringent move-limits on design variables. The objective of this research is to achieve an e$cient and accurate multipoint approximation to constraints by integrating the most accurate segment of all local approximations previously constructed. The proposed multipoint approximation is constructed by combining weighting functions with local function approximations. With function and gradient information at a series of points, local approximations are established at those points. Once established, all local approximations are blended into a multipoint approximation by use of a weighting function. Function and gradient values of this multipoint approximation correspond directly with exact counterparts at the points where the local approximations were generated. Finally, the multipoint approximation is applied to a plate and wing box thermal-structural optimization.