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."
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Still the chance of some showers in the north on Wednesday
It will become drier in the early hours setting us up for a fine start to Wednesday
Showers in the north will spread southeastwards overnight. Temperatures will be higher so not as chilly as list night.