A puncture resistant wheel apparatus, and method of use, for safely climbing obstacles are disclosed herein. A plurality of wheel apparatuses is mounted on a vehicle (e.g. a wheelchair, cart, mountain bicycle, etc.) to enable it to safely traverse obstacles, such as a flight of stairs, road curbs, etc. without slipping, and while creating a smoother ride. Each wheel apparatus comprises: a tire comprising a plurality of teeth sections separated via a thin space to grip an obstacle edge between the teeth； a circular rim attachable to the tire inner surface via T-joints, and a plurality of evenly spaced spokes extending to a central hub； and two hoop rings, mounted on opposing tire sidewalls. The center of each tire tooth section further comprises an elastic unit, comprising a vertical spring and two horizontal springs that further act to dampen the vibrational and jarring forces exerted on the wheel apparatus.
