In this study, optimum design of composite sandwich structures will be surveyed and presented using hybrid algorithm. Since, most modern payload fairings are constructed of a composite sandwich laminate, in this research the architecture of the fairing structure has been analyzed on the basis of the composite sandwich shell with a flexible core. However, from the geometrical point of view, fairing composed of two conical and cylindrical parts. Therefore, in the first phase, buckling analysis of conical composite sandwich shell has been done by using high-order theories and the obtained equations reduce to the governing equations of cylindrical sandwich shell when the semi-cone angle is set equal to zero. In the second phase, the obtained structure was optimized using hybrid algorithm. Due to the variety and complexity of design variables in composite sandwich structures, designing process leads to difficulties and obstacles in design optimization problems. Since, the most important selected discipline for optimizing the mass specifications of launch vehicle is structure, therefore with relying on optimization of the structure, after completion of optimization process, finally considerable mass reduction i.e. 40 percent comparing to the utilized fairing in this study (Fairing of Safir), will be concluded due to simultaneous changing of material and optimization.