In Greek mythology, Agamedes was a son of Erginus. With his brother, Trophonius, he built Apollo's temple at the oracle at Delphi. Once finished, the oracle told the brothers to do whatsoever they wished for six days and, on the seventh, their greatest wish would be granted. They did and were found dead on the seventh day. The saying "those whom the gods love die young" comes from this story.

Alternatively, they built a treasure chamber (with secret entrance only they knew about) for King Hyprieus of Boeotia. Using the secret entrance, they stole Hyprieus' fortune. He was aware but did not know who the thief was; he laid a snare. Agamedes was trapped in it; Trophonius cut off his head so that Hyprieus would not know who the body in the snare was.