Police are supporting the initiative, which runs across Sussex and Surrey, until Sunday, May 29.
Police said that people in possession of unwanted guns or ammunition are encouraged to hand them in.
A Sussex Police spokesperson said: “Many firearms are held in innocence and without awareness of their illegality or are overlooked and forgotten in people’s homes.
“Others are acquired and distributed by criminal networks to harm, threaten and intimidate their local communities.
“This appeal gives people the chance to dispose of firearms or ammunition by handing them in at their local police station.”
The surrender forms part of a national campaign by the National Ballistics Intelligence Service (NABIS).
The aim is to reduce the number of illegally held firearms in circulation, which could fall into the hands of criminals.
This includes replica firearms, air weapons, BB guns, imitation firearms, antique guns, component parts, stun guns, Taser, cs/pepper spray and other ballistic items.
Current and previous military personnel are also urged to hand in any items kept as war trophies.
Superintendent Graham Barnett from Surrey Police and Sussex Police Joint Operations Command said: “If you have firearms or ammunition that you don’t know how to safely dispose of, we can help.
“By surrendering your weapons now, it will prevent them falling into the hands of criminals and endangering the public.”
He said: “Whether what you have is illegal or not, and whatever and however you came to have it, if you no longer want it, please hand it in.
“I also ask anyone who knows anything about an illegal firearm and who wants to report this anonymously, to do so into Crimestoppers on 0800 555 111.”
Police said that during the two-week campaign, those surrendering firearms will not face prosecution for the illegal possession upon surrender.
They added that these measures will enhance the rights and privileges of lawful gun licence-holders by removing dangerous ones from the wrong hands.
Lawful gun licence-holders are being encouraged to use this campaign to consider the surrender of weapons they no longer have any use for.
Superintendent Barnett said: “I’d like to clarify that this is a firearms surrender and not a general firearms amnesty for the previous lifetime of the firearm; an amnesty will be granted for police possession of an item only at the point of handover (surrender).”
These are the police stations that people can use to hand in firearms:
Crawley Police Station, Northgate Avenue (Monday to Saturday, from 9am to 8pm)
Worthing Police Station, 21 Chatsworth Road (Monday to Saturday, from 9am to 8pm)
Chichester Police Station, Kingsham Road (Monday to Saturday, 9am-8pm)
Hastings Police Station, Bohemia Road (Monday to Saturday, 9am-6pm)
Eastbourne Customer Contact Point, 1 Grove Road (Monday to Saturday, 9am-5pm)
Uckfield Police Station (Monday to Friday, 10am-2pm)
Brighton Police Station, John Street (Monday to Sunday, 8am-10pm)
In Surrey the following stations are open from Monday to Sunday, from 8am-10pm: Guildford, Reigate, Staines.