In this paper, in support of developing an advanced non-pneumatic lunar tire, a dynamic interaction model between non-pneumatic tire and sand is presented using the Finite Element Method (FEM). This non-pneumatic tire is composed of three major components: a critical shear beam, two inextensible circumferential membranes, and deformable spokes. The non-pneumatic tire made of segmented cylinders is described in detail. The tire is treated as an elastic deformable body with the inertia effect is included. Lebanon sand found in New Hampshire is modeled as because of the availability of a complete set of material properties in the literature. The Drucker-Prager/Cap plasticity constitutive law with hardening is employed to model the sand. Numerical results show contact pressure distribution, distributions of various stresses and strains, deformation of non-pneumatic tire, and deformation of sand.