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This paper describes the structural analysis and optimization of stiffeners used in inner tanks for liquid natural gas (LNG) storage, so that the costs can be minimized while the critical buckling load of the inner tank still exceeds the external pressure exerted by the perlite. The original calculation of perlite pressure applied to the inner tank was based on Zick's code, which led to the overestimation of the external pressure, and consequently, an oversized stiffener. In this study, the effects of the material properties of perlite on the external pressure distribution are scrutinized, and the optimum dimensions of a single stiffener are finally obtained through a series of parametric studies. A 15% decrease in the cost of the stiffener compared with the original design is achieved.