A non-pneumatic tire for a vehicle featuring a body of elastic material and having a circumferentially-extending crown portion featuring a running surface and circumferentially-extending sidewalls joined to the crown portion. The side walls terminate in circumferentially-extending beads which are adapted to engage the rim of a vehicle wheel. A number of radially-extending and circumferentially-spaced compound-curve springs made of a composite material are at least partially embedded within the crown portion and the sidewalls. The curved springs have ends terminating within the beads of the tire body. A circumferentially-extending belt constructed of a high-strength and low stretch material is positioned radially outside of the compound-curve springs.