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Crews from Newquay, Perranporth, St Dennis, Wadebridge, Truro, Launceston, St Austell and Tolvaddon are on scene.
A spokesperson for Cornwall Fire and Rescue Service say they are using hosereel jets to put out the fire - but smoke is entering the A30 - close to the Carland Cross interchange.
Adding: "Please proceed with caution through this area. Devon and Cornwall Police and National Highways have been informed. A 50m cordon is in place and a road in the vicinity of the farm has been closed at this time."
Nearby residents are being asked to keep windows and doors closed.