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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Delyth Thomas, aged 56, was overwhelmed when her cat Chloe walked back into her house in Skewen after four years.