Officers are hunting those responsible for setting hay bales alight in two fields in Winterton and Roxby.
The first incident took place in a field adjacent to Winterton Observatory, Top Road, Scunthorpe, between 4.45pm and 5pm on Saturday, August 8.
A group of four girls and boys, thought to be aged 12 to 13 years old, were seen running from the area.
One of the girls had long blonde hair and one of the boys was said to have short brown hair and a blue and white striped T-shirt.
The second incident happened between 5.30pm and 6pm the following day, in a field to the rear of Roxby Hall Farm, Roxby.
In this case, a black Vauxhall Corsa had been seen parked in the area and officers are keen to speak to the driver.
Anyone with information is asked to call 101, quoting crime references 2131145 of August 8 or 2131121 of August 9.