First, the effect of the geometry such as the curved shape of the struts composing the truss structure of WBK is elaborated. Then, analytic solutions for the material properties of WBK and the maximum loads of a WBK-cored sandwich panel under bending are derived. A design optimization with the face sheet thickness and the core height selected as the design variables is presented for given slenderness ratios of the WBK core. Unless the face sheet thickness is limited, the optimal design to give the maximum load per weight is always found at a confluence of three failure modes, namely, face sheet yielding, indentation plastic, and core shear modeB plastic.