The two bank machines were targeted in Stonehaven and Inverurie within the space of a few hours on Sunday night.
Detectives and forensic officers were carrying out detailed examinations of both sites yesterday morning.
Police sealed off the areas with tape as investigators took photographs and searched for evidence at the scene.
The attempted thefts happened at a Clydesdale Bank branch in the town centre of Stonehaven and a Bank of Scotland building in Inverurie.
A Clydesdale Bank spokesman said: "We can confirm that the machine was damaged overnight and is currently out of service."
The incidents are the latest of a string of thefts and attempted thefts being investigated by police in the north-east of Scotland.
Police say they are keeping an open mind on whether the incidents are linked.