In this paper, the Finite Element Method (FEM) is used to model and simulate the dynamic interaction between non-pneumatic tire and sand with obstacle to investigate the influence of obstacle on performance of the non-pneumatic tire. The non-pneumatic tire consists of three major components: two inextensible circumferential membranes, a critical shear beam, and a group of deformable spokes. The non-pneumatic tire fabricated of segmented cylinders is illustrated and the FEM model for the tire is given in detail. The tire is treated as an elastic deformable body with the inertia effect included. Lebanon sand found in New Hampshire is used in this simulation because of the availability of a complete set of material properties in the literature. Modified Drucker-Prager/Cap plasticity constitutive law with hardening is utilized to model the sand. The obstacle is represented as an elastic body. The effects of tire 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.