A new metallic sandwich panel with a quasi-Kagome truss core subjected to bending load has been analyzed. First, equations of the failure loads corresponding to the eight failure modes are presented. Then, non-dimensional forms of the equations are derived as functions of three geometric variables, one material parameter (yield strain), one load index and one weight index. Failure maps are presented for a given weight index. By using the dimensionless forms of equations as the design constraints, two kinds of optimization are performed. One is based on the weight, that is, the objective function, namely, the dimensionless load is to be maximized for a given weight. Another is based on the load, that is, the dimensionless weight is to be minimized for a given load. The results of the two optimization processes are found to agree each other. The optimized geometric variables are derived as a function of given weights or failure loads. The performance of the quasi-Kagome truss as the core of a sandwich panel is evaluated by comparison with those of honeycomb cored and octet truss cored panels.