Their airguns have been confiscated.
The boys have been reported to the Children’s Reporter for consideration of further action.
Community Inspector Carol Wood of Hawick Police Station said: “These arrests are the result of a targeted and proactive police investigation.
“I want it to send a message that reckless and dangerous behaviour particularly involving firearms will not be tolerated in our community and we will employ all resources at our disposal to track down those responsible.”
The news comes ahead of an amnesty allowing owners of airguns to hand in their weapons without being prosecuted, ahead of a new gun law being implemented.
Following the passing of the Air Weapon and Licensing (Scotland)Act 2015, police are now able to provide the dates for the surrender campaign and offer guidance to officers and staff should they receive enquiries from members of the public.
The Air Weapon and Licensing (Scotland) Act 2015 will come into effect on July 1, this year.
The new law will require any person who possesses, purchases, uses, or acquires an air weapon to have a certificate to legally hold them.
However, in order to afford people time to apply for and obtain a certificate the Scottish Government have incorporated statutory instrument legislation to ensure that no person will commit an offence of possessing an air weapon without the relevant authority or certification for “a period of not less than six months from July 1, 2016”.
As a result no offence will be committed until January 1, 2017.
This surrender campaign is intended to enable members of the public who do not wish to obtain a license to dispose of their air weapons in a safe and convenient manner.
The campaign will run between the following dates: Monday, May 23 – Sunday, June 12, from 8am–9pm each day of the surrender campaign.
The public will be asked to attend nominated police stations during the campaign to surrender air weapons.
Members of the public are invited to visit the Police Scotland website for further information.