A wheel assembly includes a rigid wheel and an airless flexible tire with certain performance characteristics of a pneumatic tire. The rigid wheel includes a central portion and a plurality of circumferentially spaced mounting elements removably attached to a radially outer margin of the central portion. The tire is mounted on the wheel and engages the mounting elements such that portions of the tire not engaging the mounting elements are separated radially from the wheel by a space. The tire is configured such that portions of the tire not engaging the mounting elements flex inwardly toward the wheel when subject to ground engaging pressure, thereby minimizing ground penetration and soil disruption. The tire may include one or more tension elements embedded in the tire to increase the tire's strength and resilience.