South Wales Police said around 50 officers are deployed in the "extensive" search for Ben Thompson, including a helicopter and search dogs.
Chief Inspector Eddie Ough said he believed Ben had left the city centre to try to walk back to where he was staying that night.
He asked people in the west of Cardiff to look in their outbuildings, as "Ben may have tripped, fallen, hurt himself, be unconscious."
More top news
Professor Roger Scully of Cardiff University analyses the results of the latest Welsh Barometer Poll
Becoming cloudier from the north and west during the evening but some places continuing to see some clear spells
A council in Wales has had to pay more than £8,600 to end a hire contract for a Porsche its former boss used to drive.