Another eyewitness, tweeting as Jon B, said: "It (the plane) turned from the north by Lancing College, went to go low towards the airfield and went behind some trees below where I was.
"Then there was a crunch sound and a ball of flames and thick black smoke came up from the ground."
At the scene
BBC Sussex reporter Simon Jenkins
I'm standing on the middle of the A27 and it's deserted.
The police are taking no chances whatsoever. I've been asked to move back in case of any further explosions.
I've been speaking to people and they are absolutely stunned. The plane seems to have stalled mid manoeuvre and came crashing down on the A27.
The acrid smell and thick black smoke has just been fanning across the area and the skies are completely quiet.
A spokesman for Sussex Police said emergency services had declared a "major incident" with a number of helicopters deployed to the scene following the crash at 13:20 BST.
He said: "The casualties are all believed to have occurred on the road at this time and there are not thought to be any injuries to anyone actually on the airfield."
"The Air Accident Investigation Bureau are attending the scene and have asked anyone who has video or photographs of the plane in the time leading up to and including the crash to hold on to them and await advice as to whether they may be wanted to assist with the investigation."
The road is likely to remain closed for several hours.
Tim Loughton MP, who represents East Worthing and Shoreham, tweeted: "Tragic news that there have been fatalities at the Shoreham Air Show crash and our thoughts and prayers must be with the families and casualties."
It is the second incident at the Shoreham Airshow in recent years.
In September 2007 James Bond stuntman Brian Brown, 49, died when he crashed a World War Two Hurricane after carrying out an unplanned barrel roll at a re-enactment of the Battle of Britain.
The Hawker Hunter was a mainstay of the RAF through the 1950s and early 1960s.
First flown in 1951, the single-seat plane was used as a fighter, fighter-bomber for reconnaissance and for aerobatics.
There was also a two-seat trainer version, which served with many other air forces. Two-seater variants are still used by the RAF for training.
The Hunter Hawker was deployed in major operations such as Malaya and Suez.
The plane was also flown by an RAF display team dubbed the "Black Arrows".