Police have charged two men with serious firearms offences following a targeted investigation in southern Tasmania.

A 36-year-old man from Herdsmans Cove was arrested on Monday after a firearm was reportedly shot towards a residence on Main Road, Claremont in the early hours of the morning.

A 24-year-old man from Claremont was arrested on Tuesday in relation to the same matter, as well as an aggravated robbery and motor vehicle stealing in Rokeby on Saturday evening.

The 36-year-old man was charged with firearms offences.

The 24-year-old man was charged with aggravated robbery, motor vehicle stealing and firearms offences.

Both men appeared in the Hobart Magistrates Court this week and have been remanded in custody to reappear on 20 September.