In the present paper, the results of an approximation method named structural index used as the first step, the process of design and optimization of stiffened panel with Gaussian type surrogate model are carried out. Modeling phase is based on the finite element analyses of the structure. Nonlinear buckling load is set as the design constraint. The surrogate model is employed to reduce the number of finite element analyses in the optimization process. Therefore time of design process is reduced. Using infill points in the modeling and optimization process, converging to local optima is ensured. Introducing a novel technique, finding the global optimum of the surrogate model is guaranteed. The approach of surrogate based optimization is illustrated using two test problems. Also the sensitivity of the response to the initial sampling plan is investigated. Convergence criteria usually used in surrogate based optimization is modified to speed the convergence but is not affected the quality of the response. Design optimization process is presented for two types of stiffened panels. In type 1 stiffened panel with 4 design variables, the initial training set is constructed using 55 points. The response is obtained after addition of 5 infill points. For type 2, the initial sampling plan is selected to be 58 points. The optimization process is stopped after adding 173 infill points. Finally, obtained results are compared with the results of structural index method and an approach toward global optimum of the compression stiffened panel is introduced with the characteristics of optimum structure.