Rhipaeosaurus was first described in 1940, from a fairly complete skeleton found in the Ural Mountains of Russia. The name 'Rhipaeosaurus' comes from 'Ῥιπαεος' 'Rhipaeos), a range of mountains in Greek mythology thought to be the Urals, and 'σαυρος', meaning 'lizard'. 'Tricuspidens' refers to its three-cusped teeth.