Important factors in a casting mold are strength at the mold surface and gas permeability of the mold. This study investigates the effects of pre-pressure and sand particle hardness on gas permeability, with a constraint that the norm of a stiffness array at the mold surface should be higher than a certain value. The constitutive relation is obtained using a hypoplasticity model. This study is firstly attempted to investigate sand behavior in mold fabrication, and will give a theoretical base for fabricating better molds.