Amphicoelias (/ˌæmfɪˈsiːliəs/, meaning "biconcave", from the Greek ἀμφί, amphi: "on both sides", and κοῖλος, koilos: "hollow, concave") is a genus of herbivorous sauropod dinosaur that lived approximately 150 million years ago during the Tithonian (Late Jurassic Period) of what is now Colorado, United States. Amphicoelias was moderately sized at about 18 metres (59 ft) in length and 15 metric tons (17 short tons) in body mass, shorter than its close relative Diplodocus. Its hindlimbs were very long and thin, and its forelimbs were proportionally longer than in relatives.

The namesake fossil of the type species Amphicoelias altus, American Museum of Natural History (AMNH) 5764, is uncertain in included material. When described by Edward Drinker Cope shortly after its discovery in 1877, Amphicoelias was noted to include many back vertebrae, a single pubis, and a femur. However, after purchase and cataloging of the material by the AMNH, Henry Fairfield Osborn and Charles Mook described that the specimen had only two vertebrae, a pubis, femur, tooth, scapula, coracoid, ulna and a second femur. The additional material, not mentioned by Cope, was found close in proximity to the holotype and was similar to Diplodocus, a relative of Amphicoelias. Their assignment was questioned by subsequent authors Emanuel Tschopp et al. in an analysis of Diplodocidae.

During the description of Amphicoelias altus in 1877, Cope additionally named A. latus, for a femur and tail vertebrae. Following its description, Osborn and Mook in 1921 reidentified the material as a specimen of Camarasaurus, an assignment followed by other authors who reviewed the material. A year later 1878, Cope named the third species of Amphicoelias, A. fragillimus for a gigantic dorsal vertebra that was subsequently lost. Measuring approximately 2.7 m (8.9 ft) if reconstructed based on Diplodocus, early estimates for the length of the animal in life were between 40 and 60 m (130 and 200 ft) long. Due to the incomplete nature, such lengths–the longest of any known dinosaur and sauropod–were largely ignored. In 2018, Kenneth Carpenter renamed Amphicoelias fragillimus as the new genus Maraapunisaurus, and reclassified it from Diplodocidae to Rebbachisauridae.

In 1877, a number of fossils were discovered by Oramel William Lucas in rock outcrops in Colorado close to Cañon City. These bones, including some named Laelaps trihedrodon, Camarasaurus supremus and Caulodon, were assumed to be from the Cretaceous-era Dakota Formation by paleontologist Edward Drinker Cope, from the same age as other Laelaps fossils. Among the assortment of fossils discovered, a specimen including multiple dorsal vertebrae, a pubis, and a femur was found by Aaron Ripley, Lucas' brother-in-law, in Quarry XII. They were sent to Cope on October 21, 1877. Cope concluded they belonged to a new taxon within Sauropoda, which Cope named Amphicoelias altus in December 1877. Cope determined that the taxon would have been a sauropod related to Camarasaurus found nearby, both being large animals with lightly built vertebrae and solid limbs. Cope sold his collection of fossils to the American Museum of Natural History (AMNH) in 1895. Shortly before his death in 1897, he worked with the museum's artist Charles R. Knight to produce illustrations and paintings depicting some of his species in life, including Amphicoelias. Based on notes accompanying his sketches provided to Knight as reference material, Cope evidently considered both Amphicoelias and Brontosaurus junior synonyms of Camarasaurus supremus at this time. The specimen was given the accession number AMNH 5764, then including two dorsals, a pubis, a femur, a tooth, a scapula, coracoid and an ulna. While the forelimb material was not originally assigned to Amphicoelias, paleontologists Henry Fairfield Osborn and Charles Mook in 1921 added them to the holotype specimen on the basis that they were found in the same strata not far away, and bore differences from the Camarasaurus they were found alongside. Because of the uncertainty about the referral of these remains, in 2015 Emanuel Tschopp and colleagues hesitantly rejected the referral of the tooth, scapula and coracoid, but accepted the ulna referral. Based on collection data, the specimen was determined to have come from the Late Jurassic-era Morrison Formation, in the youngest layers, separate from those that held the Camarasaurus fossils also described by Cope.

Cope listed multiple features to separate Amphicoelias and A. altus from their relatives. Unlike in Camarasaurus, the centra of dorsals did not have an opisthocoely, where the front end has a ball that fits into the socket of the preceding vertebra. Instead, Amphicoelias had amphicoelous vertebrae, where both ends are mildly to moderately concave. Because of this difference, Cope named two separate families to contain the different morphs of vertebral centra, one being Camarasauridae and the other being Amphicoeliidae. As well, Camarasaurus possessed pleurocoels (openings in the side of the centrum) that were taller than long-contrasting to the condition in Amphicoelias- and a more robust pubis and femur. However, both families also had accessory articulations in the neural arch, which Cope termed the hyposphene, limiting the motion of vertebrae respective to one another. Amphicoeliidae and Amphicoelias were both found to be intermediate and poorly defined by paleontologist Othniel Charles Marsh in 1881, wherein the primary feature-two mildly concave articular faces-was shown to be widespread and also found in sauropods like Brontosaurus excelsus.

Amphicoelias latus was named in the same description as the type species, Amphicoelias altus. It was named for a series of four caudal vertebrae and a femur (AMNH 5765), in relatively good preservation. The caudals are bi-concave like the dorsals of A. altus, with short centra, long prezygapophyses and shallow pleurocoels. The femur is extremely robust, as well as being wide but short front-to-back. The femur is 1.4 m (4.6 ft) long, but the very proximal end is not fully preserved. Due to the robusticity of the femur Osborn & Mook in 1921 referred Amphicoelias latus to Camarasaurus supremus, making C. supremus the valid name for the material once called A. latus.

The third named Amphicoelias species, A. fragillimus, was known only from a single, incomplete 1.5 m (4.9 ft) tall neural arch, either last or second to last in the series of back vertebrae. Based only on an illustration published in 1878, this vertebra would have measured 2.7 meters (8.9 ft) tall in life. However, it has been argued that the scale bar in the published description contained a typographical error, and the fossil vertebra was in fact only 1.38 meters (4.5 ft) tall. In addition to this vertebra, Cope's field notes contain an entry for an "[i]mmense distal end of femur”, located only a few tens of meters away from the giant vertebra. It is likely that this undescribed leg bone belonged to the same individual animal as the neural spine, but it was never collected or described. In 2018, A. fragillimus was given its own genus, Maraapunisaurus, and reclassified as a primitive rebbachisaurid.

In 2010, an article was made available, but not formally published, by Henry Galiano and Raimund Albersdorfer in which they referred to the new species "A. brontodiplodocus" to Amphicoelias, based on several complete specimens found in the Dana Quarry of Big Horn Basin, Wyoming and held in a private collection. The specific name referred to their hypothesis based on these specimens that nearly all Morrison diplodocid species are either growth stages or represent sexual dimorphism among members of the genus Amphicoelias, but this analysis has been met with skepticism and the publication itself has been disclaimed by its lead author, explaining that it is "obviously a drafted manuscript complete with typos, etc., and not a final paper. In fact, no printing or distribution has been attempted".