Alan Stewart, 55, was the first police officer to attend the lane in Greenock, Inverclyde, where the 17-year-old's remains were found in June 1986.
The High Court in Edinburgh heard how Mr Stewart - who was a police constable - saw the teenager's body lying on the ground. Her clothes were lying nearby.
Mr Stewart told prosecution advocate John Scullion: "I saw the naked body of a female. She was lying on her side. Some clothes were nearby. I remember a blue leather jacket, a black and white floral dress and a pair of shoes."
Mr Stewart was giving evidence on the second day of proceedings against 49-year-old John Docherty.
Mr Docherty, of Dunoon, Argyll, denies murder.
Mr Stewart - who became a Detective Constable with the Scottish Crime Drug Enforcement Agency - told Mr Scullion that he was on duty on June 2 1986.
He was driving around the west end of Greenock when he was instructed to go to a lane off the town's Ardgowan Street. The court heard that June 2 was a public holiday.
Once there, a member of the public, who had earlier telephoned police, told him where Elaine's body was located.
Mr Stewart - who retired from the police in September last year - told the court that Elaine's clothes were lying beside her remains.
During his evidence, the jury were shown photographs of the location where Elaine's body was found.
They were also shown video footage of the area which was also taken on the same day. In the footage, jurors could see Mr Stewart, who was wearing an old-style police uniform.
When defence advocate Donald Findlay asked Mr Stewart whether there was any doubt as to whether Elaine was dead, Mr Stewart replied: "No."
The court heard that Mr Stewart then secured the area and made a log of the policemen visiting the scene. The jury also heard that a firm of undertakers removed Elaine's body later in the day.
The court also heard evidence from another retired police officer, William Kennedy, 56, who was at the location where Elaine's body was discovered.
The jury heard that he was told by a senior CID officer to cover Elaine's body with a blanket, which was taken from a police car. The court heard that the blanket could have "contaminated" or "decontaminated" evidence from Elaine's remains.
When Mr Findlay asked Mr Kennedy what he knew about crime scene contamination in 1986, Mr Kennedy replied: "Next to nothing, to be honest."
Mr Docherty has pleaded not guilty to murder. He also denies stealing a handbag. He further denies a charge of attacking another woman, Linda Hargie, on occasions between 1990 and 1995 at an address in Greenock.
As the trial began on Friday, the jury heard Mr Findlay had given the court notice of Mr Docherty's alibi.
Another document lodged by the defence stated that Mr Docherty denied murder and theft and blamed the crime on "person or persons unknown." The so-called special defence of incrimination claimed the culprit might be among a list of names taken from files of the police investigation into the alleged murder. A total of 41 names were read to the jury.
The trial continues.