A non-pneumatic tire has a crown region and a pair of sidewall regions, including a first sidewall region and a second sidewall region. The non-pneumatic tire includes a pair of beads, including a first bead and a second bead, and a toroidal element. The toroidal element includes an inner region, an outer region, and a central region. At least a portion of the central region is more elastic than the inner and outer regions. The toroidal element includes a crown portion extending across the crown region of the non-pneumatic tire, a first sidewall portion extending along at least a portion of the first sidewall region of the non-pneumatic tire, and a second sidewall portion extending along at least a portion of the second sidewall region of the non-pneumatic tire. The toroidal element is pre-stressed such that when the non-pneumatic tire is mounted to a rim, the first sidewall portion of the toroidal element exerts a first axially outward force of at least 1000 pounds against the rim, and such that the second sidewall portion of the toroidal element exerts a second axially outward force of at least 1000 pounds against the rim.