Mid and West Wales Fire and Rescue Service says 11 of its crews are continuing to fight the fire at the National Library of Wales.
It is advising people "to stay away for safety."
This video - from viewer Edward Mulgrew - shows firefighters pumping water onto the library roof earlier.
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Swansea relieved the pressure on under-fire manager Bob Bradley with an emphatic 3-0 home victory over fellow strugglers Sunderland.
Sol Bamba was sent off after losing his cool but Cardiff hung on to claim a deserved 1-1 draw at Ipswich.
Today's rain will soon clear south-eastwards to leave a largely dry night with some long clear spells.