Windows have been smashed with rocks and bricks and a vehicle has been set on fire in a High Wycombe street.
Between Saturday, April 1 and yesterday (May 9), 11 incidents of criminal damage and one of arson were committed on a house in Chiltern Avenue.
During the attacks, three people broke windows by throwing rocks and bricks and setting fire to a vehicle.
Fortunately, no one was injured during the incidents.
C/Insp Graham Hadley, Deputy Commander for Wycombe Local Police Area, said: "This has understandably been a very distressing time for the homeowners and we are actively investigating these incidents.
"I would like to appeal directly to the community for their help in bringing those responsible to justice.
"If you have any information regarding these incidents, no matter how small, please contact us via the Thames Valley Police enquiry centre on 101."
To give information anonymously, call Crimestoppers on 0800 555 111.