The nonpneumatic tire (NPT), as the name suggests, is a type of tire that does not use air to support the load. Because of their outstanding advantages, such as durability and low rolling resistance, these tires have attracted much interest. The study of NPTs has drawn considerable recent attention, and some research was conducted to investigate their mechanical response. However, these studies did not consider an analysis of an NPT against obstacles. Therefore, in this article, the static and dynamic behaviors of an NPT with honeycomb structures rolling over different obstacles are investigated using numerical simulation. The flexible spokes, which are the most important part of NPTs, are assumed to have a honeycomb structure with the same cell wall thickness and angle. Based on the mesostructures hypothesis, these spokes are considered to be made of polyurethane material. To perform a more precise analysis, various parameters such as nonlinear properties of the material and contact condition are taken into account to establish the finite element model. The results, which can be used as a benchmark and are suitable for design purposes, are presented elaborately.