In this paper, the Finite Element Method (FEM) is used to investigate the tread profile effects on the performance of the cellular shear band-based non-pneumatic tire when interacting with sand for the NASA's new Moon mission. This non-pneumatic tire consists of three major components: a critical cellular shear band, two inextensible circumferential membranes, and a group of deformable spokes. The cellular shear bands made of an aluminum alloy (AL7075-T6), are designed to have the same effective shear modulus of 6.5E+6 Pa. In this research, the shear band with cellular geometry of (θ = -65°, h = 21) is used. The Lebanon sand found in New Hampshire is used in this research and Drucker-Prager/Cap plasticity constitutive law with hardening is employed to describe the behavior of the sand. The tire and treads with different profiles are treated as deformable elastic bodies. Penalty contact algorithm is used to model the tangential behavior of the contact between the tread and sand and Coulomb's law is considered for the friction between tire and sand. Numerical results show the deformation of sand and tire. The stress (strain) distribution in sand, tire, treads with different profiles, and along the interface between them is also presented. The effect of the tread profile on the contact pressure between tire and sand is explored.