Inconel 690 for nuclear steam generator tube has more Chromium than the conventionally used Inconel 600 in order to increase the corrosion resistance. To evaluate the tribological characteristics of Inconel 690 under fretting condition the fretting tests were carried out in air and elevated temperature water. Fretting tests of the cross-cylinder type were done under various vibrating amplitudes and applied normal loads in order to measure the friction forces and wear volumes. From the results of fretting wear tests. the wear of Inconel 690 can be predictable using the work rate model. The amounts of friction forces were proportional to relative movement between two fretting surfaces. The friction coefficients were decreased as increasing the normal loads and deceasing the vibrating amplitudes. Depending on fretting environment, distinctively different wear mechanisms and often drastically different wear rates can occur It was found that the fretting wearfactors in air and water at 2$0^{circ}C$, 5$0^{circ}C$, and 8$0^{circ}C$ were 7.38 $ imes$ $10^{-13}$$Pa^{-1}$, 2.12 $ imes$$10^{-13}$$Pa^{-1}$, 3.34$ imes$$10^{-13}$$Pa^{-1}$and 5.21$ imes$$10^{-13}$$Pa^{-1}$, respectively flexibility to model response data with multiple local extreme. In this study, metamodeling techniques are adopted to carry out the shape optimization of a funnel of Cathode Ray Tube, which finds the shape minimizing the local maximum principal stress. Optimum designs using two metamodels are compared and proper metamodel is recommended based on this research.