To facilitate the design of a non-pneumatic tire for NASA's new Moon mission, the authors used the Finite Element Method (FEM) to investigate the interaction between soil and non-pneumatic tire made of different cellular shear bands. Cellular shear bands, made of an aluminum alloy (AL7075-T6), are designed to have the same effective shear modulus of 6.5E+6 Pa, which is the shear modulus of an elastomer. The Lebanon sand of New Hampshire is used in the model. This sand has a complete set of material properties in the literature and Drucker-Prager/Cap plasticity constitutive law with hardening is employed to model the sand. The tires are treated as deformable bodies, and the authors used the penalty contact algorithm to model the tangential behavior of the contact. The friction between tire and sand is considered by using Coulomb's law. Numerical results show deformation of sand and tire. The stress (strain) distributions in sand, tire, and along the interface between them are also presented. In addition, the effect of the orthotropic properties of cellular material on the contact pressure between tire and sand is explored. Numerical results show that the shear band with cellular geometry of (θ = -65°, h = 21) is great most promising for use in the non-pneumatic tire.