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In this paper, dynamic impact between cellular shear-band-based non-pneumatic tire and sand with obstacle is investigated by using the Finite Element Method (FEM) for the NASA's new Moon mission. In this research, the shear band with cellular geometry of (cell angle θ = -65°, cell height 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 obstacle is represented as an elastic body. Penalty contact algorithm is used to model the tangential behavior of the contact between the tire and sand. Coulomb's law is considered for the friction between tire and sand. Numerical results show the deformation of sand and tire. The effects of the running speed on the deformation of tire and sand, stresses and strains of the tire and sand, vertical accelerations of the hub center, horizontal reaction forces of the hub center are presented.