A 17 year old boy from Hampshire and a 54 year old man from Salisbury have been arrested on suspicion of burglary offences, following an incident near Amesbury.
The pair have been questioned by detectives, who are investigating what happened on Tuesday 9th April.
Police say enquiries identified a vehicle which had been witnessed in the area at the time of the theft and due to the fact that a shotgun had been stolen, armed officers were deployed in the search for the vehicle.
At around 5.45pm the vehicle was spotted being driven on the A36 towards Salisbury from the Southampton direction and armed officers were deployed to stop the car.
Following a search of the vehicle, the driver, a 54-year-old man from Salisbury, was arrested on suspicion of burglary, possession of an offensive weapon and possession of criminal property.
No firearm was recovered from the vehicle and due to this, a further search was conducted by armed police in the Odstock area later that evening.
A 17-year-old boy from Hampshire was later arrested on suspicion of burglary, theft and possession of criminal property.
Sergeant John Hutchings, sector deputy for Wiltshire South Community Policing Team, said:
"Unfortunately the shotgun is still outstanding and I would urge anyone with any information regarding its whereabouts or if you have been approached within the last 24 hours by someone selling a shotgun in suspicious circumstances, to please contact us.
"It is vital that such a weapon does not remain outstanding and any information however small, could assist us in the successful recovery of the property."
Anyone with information should call Wiltshire Police on 101, quoting crime reference number 54190034633.