In Greek Mythology, Acastus was one of the men who sailed with Jason and the Argonauts. His father was Pelias, then king of Ioklos who was later killed thanks to a trick by Medea. In revenge, Acastus drove Jason and Medea into exile, and so became king of the country himself.

Acastus purifed Peleus of the murder of King Eurytion of Phthia Then, Peleus lost a wrestling match in the funeral games of Pelias to Atalanta. Astydameia, Acastus' wife, fell in love with Peleus but he scorned her. Bitter, she sent a messenger to Antigone, Peleus' wife and daughter of Eurytion, to tell her that Peleus was to marry Acastus' daughter, Steropes; Antigone hanged herself.

Astydameia then told Acastus that Peleus had tried to rape her. Acastus took Peleus on a hunting trip and hid his sword, then abandoned him right before a group of centaurs attacked. Chiron, the wise centaur, returned Peleus' sword and Peleus managed to escape. He pillaged Ioklos, sometimes said to have been helped by Jason and the Dioscuri, and dismembered Astydameia, then marched his army between the pieces. Acastus and Astydameia were dead, and the kingdom fell to Jason's son Thessalus.

Acastus and Astydameia had one daughter besides Sterope: Laodamia. Another daughter Stenele is given by Apollodorus of Athens as the wife of Menoetius and mother of Patroclus.