In Greek mythology, Elasippus (Ancient Greek: Ἐλάσιππον means 'horse-riding, knightly') may refer to two personages:

Elasippus, one of the ten sons of Poseidon and Cleito in Plato's myth of Atlantis.Plato, Critias 113d He was the elder brother of Mestor and his other siblings were Atlas and Eumelus, Ampheres and Evaemon, Mneseus and Autochthon, and lastly, Azaes and Diaprepes.Plato, Critias 114a–c. Elasippus, along with his nine siblings, became the heads of ten royal houses, each ruling a tenth portion of the island, according to a partition made by Poseidon himself, but all subject to the supreme dynasty of Atlas who was the eldest of the ten.Plato, Critias 114d. Elasippus, son of Haemon and an Achaean soldier who participated in the Trojan War. He was slain by the Amazon queen, Penthesilia.Quintus Smyrnaeus, Posthomerica 1.229.

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References

Plato, Critias in Plato in Twelve Volumes, Vol. 9 translated by W.R.M. Lamb. Cambridge, Massachusetts, Harvard University Press; London, William Heinemann Ltd. 1925. Online version at the Perseus Digital Library. Greek text available at the same website. Quintus Smyrnaeus, The Fall of Troy translated by Way. A. S. Loeb Classical Library Volume 19. London: William Heinemann, 1913. Online version at theio.com Quintus Smyrnaeus, The Fall of Troy. Arthur S. Way. London: William Heinemann; New York: G.P. Putnam's Sons. 1913. Greek text available at the Perseus Digital Library.