Abstract: A non-pneumatic support structure for a wheel having an axis of rotation for use in tires and wheel assemblies for a vehicle is provided. The non-pneumatic support structure includes one or more anisotropic parabolic discs. The one or more anisotropic parabolic discs are configured to allow deformation parallel to an axis of rotation of the wheel with the ground and to substantially favor lateral deformation over radial deformation. The non-pneumatic support structure may be incorporated into a tire, or an indivisible tire and wheel assembly. A tire or tire and wheel assembly incorporating a non-pneumatic support structure includes a radial ground contacting tread. Further, a tire or tire and wheel assembly incorporating a non-pneumatic support structure will deform parallel to the axis of rotation in response to impact, load or shear to increase the area of the ground contacting tread in contact with the ground.