In Greek mythology, Epaphus (Ἔπαφος), also called Apis, was the son of Zeus and Io. He was also a king of Egypt.
The name/word Epaphus means "Touch". This refers to the manner in which he was conceived, by the touch of Zeus' hand. He was born in Euboea (Herodotus, Strabo) or, according to others, in Egypt, on the river Nile, after the long wanderings of his mother. He was then concealed by the Curetes, by the request of Hera, but Io sought and afterward found him in Syria.
Epaphus is regarded in the myths as the founder of Memphis, Egypt. With his wife, Memphis (or according to others, Cassiopeia), he had one daughter, Libya. Another of his daughters bore the name of Lysianassa.
Epaphus also criticized Phaëton's heraldry, which prompted him to undertake his fateful journey in his father Phoebus' chariot of the sun. Belus, another mythological king of Egypt, is a grandson of Epaphus.
David Rohl identifies Epaphus as the Hyksos pharoah Apophis.