Ten properties have been targeted in a spate of incidents involving a pellet gun or similar weapon.
The incidents in the Buchan and Formartine areas of Aberdeenshire resulted in windows being damaged.
Homes and commercial premises in the Ellon, Oldmeldrum, Hatton, Boddam and Cruden Bay areas were targeted as well as properties on the A90 and A975.
Police have appealed for information about the attacks which happened between Thursday and Monday.
Sgt Richard Barnwell said: "This kind of behaviour is completely unacceptable and will be robustly investigated.
"The properties appear to have been randomly targeted and those responsible have shown complete disregard for the impact this could have on the occupants within.
"It is likely that the suspects have been using a vehicle to drive around the area and shoot projectiles at windows of these properties, situated on the main roads. If you witnessed anything of this nature, or have dash-cam footage which could assist our inquiries, please get in touch."