The airmen tramped through Rendlesham Forest in search of the source of mysterious night-time lights that looked like an alien spacecraft.
It became one of the world's most famous UFO sightings - and has never been explained.
The tape begins with an American noting that local farm animals were behaving strangely.
He says: "They're very, very active, making a lot of noise.
"Straight ahead. There it is again. Straight ahead. What is it? A strange, small red light.
"It looks maybe half a mile further ahead. There is no doubt about it, it is a strange flashing red light ahead."
He continues: "I saw a yellow tinge in it too. Weird. It's coming this way. It's definitely coming this way.
"There is no doubt about it - this is weird."
The servicemen were led by Colonel Charles Halt, of the local US Air Force Bentwaters base.
He reported the December 1980 incident to the Ministry of Defence.
Damage to trees was later found 18ft high.
Theories range from an accident cover-up to lighthouse beams.
Voeg toe aan: