The 48-year-old from the Bath Street area of Glasgow is a student at Glasgow Kelvin College and was last seen there by staff at around 11.55am on Thursday 15 December 2016.
Ms Cairns is described as white, 5ft 4, slim build, shoulder length black hair, brown eyes and has a pierced upper lip. She was wearing a black leather jacket with a fur hood, light coloured top, shiny silver trousers, black calf length boots and was carrying a large black square shaped bag.
Sergeant Michael Fletcher at Glasgow City Centre Police Office said: “It is unusual for Elizabeth to be missing for this length of time and as such her family and friends are becoming increasingly concerned.
“I urge anyone who has seen Elizabeth since lunch time on Thursday 15 December or anyone who knows of her present whereabouts to contact police immediately.
“I’d also like to appeal to Elizabeth herself to contact either her family or police to let us know that she is safe.”
Anyone with information is asked to contact Glasgow City Centre Police Office via 101.