On Monday evening several windows were smashed at Bankier Primary in Banknock.
The school has CCTV cameras and their footage revealed that, at 4.55pm, two boys climbed on to the roof of the building.
Although there is no record of the damage taking place, police are keen to trace the children.
They were both white and aged 10-12. One had dark hair and was wearing just dark shorts and black trainers, while the other had fair hair and had blue jeans and a white t-shirt on.
Anyone who has information can contact police on 101.