A resilient wheel and a method for traversing an obstruction therewith are disclosed. The wheel comprises a hub assembly, a flexible rim, and a spoke band assembly extending from the hub assembly to the flexible rim to form spokes. Each spoke has a spoke length defined to be a distance along the spoke from a point of contact of the spoke on the flexible rim to a point of origin of the spoke at the hub assembly. The spoke band assembly is configured such that contact of the flexible rim with an object as the wheel moves forward causes the spoke length of a number of the spokes to shorten and the spoke length of an equal number of the spokes to lengthen.