Urgent measures are being taken to preserve the ancient trees
Archaeologists found the 16 preserved trunks in an open cast coal mine in the north-eastern city of Bukkabrany.
The specimens were preserved intact while most of the forest turned to coal thanks to a casing of sand, which was perhaps the result of a sandstorm.
It is hoped the trees may offer experts a valuable insight into Earth's climate eight million years ago.
The massive trunks are of a species known as swamp cypresses, which grew for 200-300 years.
The BBC's Nick Thorpe in Budapest says the wood of the trees is still brown in photographs taken by the archaeologists, giving the impression that it has only just been split.
The stumps, 2-3m (10ft) in diameter and 6m (19ft) high, stand uncovered on the lowest level of the mine.
However, now that the protective material around them has been stripped there is a danger that the trunks could turn to dust before the scientists' eyes.Urgent measures are being taken to preserve them after an attempt to move one of the trunks failed.