It follows more than 340 complaints to police last year of cars being raced, loud music and antisocial behaviour.
The order gives police extra powers to disperse groups of more than two people who have or could cause alarm, distress, harassment or intimidation.
The orders come into force on 1 February and run for six months.
NEW DISPERSAL ZONES
An Avon and Somerset Police spokesman said people who live near the car parks have had their lives made a misery by the car enthusiasts.
"They turn-up in numbers, play loud music, rev their engines and race. All of this has been happening late at night and really ruining the residents' quality of life.
"We've tried giving warnings and fixed-penalty notices and projects like the sparkplug initiative to educate them.
"None of these efforts have had an impact on reducing the disruption caused to local people by these young drivers," said Sgt Jim Waugh.
Mendip District Council, who approved the police application for the orders, said it was confident the initiative would go some way to addressing the issue.
"Dispersal areas will help us to reduce antisocial behaviour and noise problems in our car parks - mainly caused by boy racers
"It's a problem that we have in a number of our car parks and we receive numerous calls from those who are concerned about the nuisance particularly in the spring and summer months," spokeswoman Jenny Davies said.
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