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South East Coast Ambulance Service said the victims all died at the scene, with a further person being taken to hospital in critical condition.
The plane crashed on the nearby A27 in West Sussex. The road is likely to remain closed for several hours.
Eyewitnesses said the plane was performing a loop but did not complete the manoeuvre and crashed.
Stephen Jones, who saw the crash, said: "The aeroplane involved is a Hawker Hunter T mark 7. And he'd just begun his flying display.
"He'd gone up into a loop and as he was coming out of the loop I just thought, you're too low, you're too low, pull up.
"And he flew straight into the ground either on or very close to the A27, which runs past the airport."