Two people on a tour bus used by the American band Baroness were injured when the vehicle they were in fell 30ft (10m) from a viaduct near Bath.
Emergency services were called to Brassknocker Hill, in Monkton Combe, on the B3108 at its junction with the A36 Warminster Road at 11:30 BST.
Agents for the band, which were due to appear in Southampton later, have confirmed the accident.
The group played at The Fleece in Bristol on Tuesday evening.
Baroness's tour promoter said: "It is with great regret that we have to inform you that Baroness were involved in a very serious road accident earlier today and will not be able to perform at Talking Heads tonight.
"Our thoughts are with the band at this time and we wish them and their crew a speedy recovery."
The band was formed in 2003 in Savannah, Georgia, and has toured throughout Europe and the United States.
They have also played at a variety of festivals, including Coachella and Bonnaroo in the United States.
An Avon and Somerset Police spokesman said the incident involved a coach which had left the road with approximately nine passengers on board.
'Fallen off viaduct'
The fire service said both of the trapped victims had now been released by firefighters.
"Those people are now being treated by ambulance staff," a spokesman said.
"There were seven other passengers on board the coach, who have also been receiving medical treatment."
One eyewitness, from the Angel Fish restaurant on the viaduct, said she could see the coach on its side.
"The coach has overturned and fallen off the viaduct at the traffic lights on the A36," she said.
Low visibility
Great Western Ambulance Service said two of the injured people on board the coach have been taken to Frenchay Hospital in Bristol while seven others went to the Royal United Hospital in Bath.
"Our staff assessed all occupants and provided any required treatment before and while en route to hospital," a spokesman said.
Insp Nick Hunt, from Avon and Somerset Police, added: "Police are investigating the circumstances of the accident. At this stage it is too early to tell what the cause was."
Heavy rain in the area reduced visibility and it was not possible for the air ambulance to land.
The A36 has been closed between Bath and its junction with the A366 at Farleigh Hungerford.
Brassknocker Hill is also closed and motorists have been asked to avoid the area.
