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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The rain may become increasingly patchy later in the afternoon, perhaps allowing some drier and brighter interludes.
Cloudy skies overnight, accompanied by patchy rain through the first part of the night.
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