Lucy Holmes was last seen on Wednesday, at around 5.30pm, outside the Magnum Bar in Albany Street.
She was in the company of an unknown male.
Since then, she has not been in touch with friends or family, and police are growing concerned for her welfare.
She is described as white with a tanned complexion, medium build, around 5ft 6ins tall and with long, black hair.
She was last seen wearing a three-quarter-length jacket and carrying a brown Michael Korrs handbag.
Those with information should contact Police Scotland on 101.