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
Wales's vote to leave the European Union should not damage Cardiff's reputation as a 'inclusive' city, say council officials.
The two men who ran Wales Stronger in Europe have revealed where they think the campaign went wrong -and call for Jeremy Corbyn to resign.
After a dry start for many, rain will quickly spread across the country turning heavy in places, most likely in the north and west.