Duncan Sim, 19, has not been in contact with friends or family since leaving an event at Madras Rugby Club in the Fife town at about 11.15pm on Wednesday, March 14.
The first year chemistry undergraduate was due to arrive at another venue with a group of fellow students.
The alarm was raised after the teenager failed to return to his halls of residence the next morning. Friends described his disappearance as completely out of character.
Chief superintendent Colin Gall said yesterday the search for Mr Sim was now a divisional priority for Fife police, with other regional and national divisions sending assistance. A helicopter was deployed to aid officers on the ground.
Police have also released CCTV from the night showing the suit and tie Mr Sim was wearing when last seen.
He is white, 6ft, of medium build, with brown hair and green eyes.
Chief inspector Steven Hamilton said: “Duncan has now been missing for a significant amount of time and we are very concerned for his welfare.
“The response from the public and our partner agencies has been fantastic, and we are thankful for their support as we continue in our efforts to trace Duncan.
“I would appeal specifically to anyone who may have seen Duncan, or a man matching his description, outside Madras rugby club at around 11.15pm on Wednesday night.
“We have released an image of Duncan from earlier in the evening showing the clothing he was wearing when last seen.
“I would ask the public to view this image and come forward if they saw Duncan after 11.15pm on Wednesday evening.
“I would also ask local residents in the St Andrews area to check their gardens, outbuilding and cars as Duncan may have entered to seek shelter and which can help us establish his current whereabouts.”
Hundreds of people, including many from the student’s hometown of Duns in the Scottish Borders, have formed search parties in St Andrews and the surrounding area.
Madras Rugby Club captain Ben Peddie has led the volunteer effort. “Our holiday started on Friday but people delayed their journeys home just so they can help,” he told the BBC.
“We’ve had huge number of Duncan’s community from the Borders coming up to help too. Hundreds of us have been searching open land, farm land, verges. We went seven miles out of town and back in and had about 200 people out helping with the efforts.
“We are making sure we are here for everyone who is wondering where Duncan is. We’ve got groups looking after each other really.
“We are using Madras clubhouse as a hub for people who want to come in and have a chat. Businesses and the university have been very great in providing food and drinks for us.”
Those with information can contact St Andrews Police Station via 101, quoting incident number 2987 of 15 March.
Meanwhile, Mr Sim’s relatives have hit out at fake Facebook pages which were set up in the wake of his disappearance.
Profile pages, pretending to be that of the teenager, were set up using pictures of him. Friend requests were then sent to relatives.