The burglary happened at a house in the Glenburn Road area of Larne on Tuesday, August 16.
Detective Sergeant Peter Crothers said: “At approximately 2:45 pm, we received a report that three masked men entered a house in this area.
“They broke into a gun cabinet and stole a shotgun, air rifle and ammunition. A sum of cash was also stolen.
“The males made off in a silver Seat Leon car, registration number NHZ8403, which was later found burnt out in the Ballyboley Road area.
“It is believed the vehicle was stolen during a creeper burglary in the Ballycoose Road area sometime between Sunday 14th August and Monday 15th August.
“Detectives are investigating and would appeal to anyone with information, or anyone who was in the area at the time and witnessed any suspicious activity, to contact them on 10.
“Alternatively. information can be given to the Crimestoppers charity anonymously on 0800 555 111.”