Jordan Sullivan, 19, was last seen at approximately 9.30am on Tuesday 14 February 2012, near the River Ouse in Naburn. He removed his clothing and ran towards the river.
Police, the North Yorkshire Fire and Rescue Service and air support have made an extensive search of the area but have so far been unable to locate Jordan.
He is described as white, approximately 5ft 9in tall with a slim build and short dark hair. Jordan also has a tattoo of a crucifix running between his shoulder blades.
PC Alex Dobson, of York Safer Neighbourhood Team, said: “I am urging anyone who may have seen a naked man in area to contact the police immediately.
“I am also appealing to anyone who may have seen any unusual activity near the River Ouse.
“Jordan, if you see or hear this appeal please get in touch as I need to ensure that you are safe and well.”
If you can help to locate Jordan Sullivan please ring North Yorkshire Police on 101 and select option 1.