Sauropod dinosaurs achieved the largest body sizes and the most elongate necks and tails of any terrestrial vertebrate. The elongate, cantilevered necks of sauropods comprised opisthocoelous vertebrae joined at concavo-convex joints. Opisthocoelous centra also occurred in the dorsal region of sauropods and procoelous centra in the tails of certain lineages. Concavo-convex intercentral joints have been hypothesized to increase the flexibility of the vertebral column or to stabilize intervertebral joints against shear stresses. Using Alligator as an extant analog, condyle convexity and range of motion were measured at every intervertebral joint in an individual, with the latter measured in situ. Results reveal that convexity is greatest in the alligator presacral column where flexibility is low; amphiplatyan vertebrae occur in the distal caudal region where flexibility is highest. The negative relationship between convexity and flexibility is not significant, indicating that flexibility is independent of centrum articular morphology. Convexity is greatest in regions in which high shear stresses are predicted to result from terrestrial locomotion and tail flexion. The evolution of opisthocoelous cervical vertebrae in early sauropods likely strengthened the long and massive neck against catastrophic dislocations without compromising joint mobility. The stabilization provided by dorsal opisthocoely and caudal procoely may relate to clade-specific specializations such as the “whiplash” tails of flagellicaudatans and the “wide-gauge” limb stance in titanosaurs. The study of opisthocoely and procoely provides a means to understand the loading regimes of the vertebral column in sauropods and other vertebrates, with implications for the behavior and ecology of fossil taxa.