A non-pneumatic tire comprising side cavities that are staggered with respect to laterally opposing side cavities, and laterally extending tread grooves that are in substantial radial alignment with the cavities. In another embodiment, the invention is to a tire comprising side ribs that are staggered with respect to laterally opposing side ribs, and laterally extending tread grooves that are substantially offset relative to the side ribs. Also provided are processes for making such tires and to off-the-road (OTR) vehicles employing such tires.