The search for the remains of Peter Wilson is taking place at Red Bay in the village of Waterfoot in the Glens of Antrim.
The Commission for the Location of Victims' Remains began the search yesterday afternoon at a site beside the sea, about 250 metres from a caravan park.
Excavation is expected to begin next week.
This is the first time a dig for one of 'the Disappeared' has taken place in Northern Ireland, and also the first time such a search operation has taken place in a built-up area.
Peter Wilson was 21 years old when he went missing. He was last seen in the Falls Park area of west Belfast on 3 August 1973.
Mr Wilson had four sisters and one brother and lived in the St James' area of Belfast. His father, Henry, died within a year of his disappearance. His mother, Elizabeth, died in 2007.
In a statement, the Wilson family said they had waited a long time for today, and were relieved that a search for Peter's body was now under way.
They said they had often visited the beach at Waterfoot with their mother, never knowing that Peter's body might have been buried there.
They said they prayed the search would bring closure to the family, and looked forward to being able to give Peter a Christian burial.
The development follows the discovery of human remains at a site in Carrickrobin, Co Louth, earlier this month.
The family of 24-year-old Gerry Evans, who disappeared in 1979, are awaiting formal identification of the body.
Last July, the remains of another of the Disappeared, Charlie Armstrong, were discovered in bogland in Co Monaghan.
The commission is responsible for finding the remains of the men and women abducted, murdered and secretly buried by paramilitaries during the Troubles.
The remains of seven people have so far been found south of the border.