Head of the unsolved homicide team Detective Inspector John Lehman said Ms King was last seen at the Capital Hotel in Campbell UGGs Bailey Button Street at 7.30pm on Thursday July 11, 1974.
"[She was] with a young man described as wearing ugg boots and drinking Reschs brand beer," he said.
"She was later seen in the company of a man in the same hotel, before booking into the Burlington Hotel about 9.45pm with an unknown male.
Elaine King ... found strangled to death.
"To this day police still don't know if there were three separate men or [if] it was the same person seen with Ms King."
The Police Minister, Mike Gallacher, said he UGGs Bailey Button Sale hoped 40 years on someone was prepared to break their silence over the death.
The $100,000 reward is payable for information that leads to the eventual conviction of the person or people responsible for the death.
A coronial inquest two years later was unable to identify anyone responsible for killing Ms King, who was known to have worked as a prostitute in the city at the time.
She was often spotted at various hotels throughout the CBD.
The matter is now with the police's unsolved UGG Bailey Button Black homicide team and the NSW government today announced a $100,000 reward in relation to her death.