In Greek mythology, Cercaphus was one of the Heliadae, sons of Helios and Rhodus. He and his brother Ochimus were the only one to stay at the island of Rhodes, after their brother Tenages was killed by the other four and the murderers had to escape.
Ochimus, the eldest of the seven, became the king of Rhodes. Cercaphus married his niece Cydippe (or Cyrbia), daughter of Ochimus and Hegetoria, and subsequently inherited the island. According to an alternate version, Ochimus engaged Cydippe to Ocridion but Cercaphus loved her and kidnapped her. He did not return until Ochimus was old.
Cercaphus and Cydippe had three sons, Lindus, Ialysus and Camirus. After their father's death and a devastating deluge, they divided the island among themselves, and each founded a city and named it after himself (modern Lindus, Ialysos and Kameiros).