They struck at Netherthorpe Airfield in Thorpe Salvin between 7pm and 9pm on Wednesday 3rd June. causing damage which will cost over £500 to repair.
Officers want to speak to anyone in the area at the time who might have seen anyone acting suspciously.
PC Gary Scott said: “Causing damage to aircraft is extremely serious.”
“Even minor damage can seriously alter an aircraft’s flight capability and potentially causing it to malfunction whilst in flight.”
Anyone with information is being asked to call South Yorkshire Police on 101.
Alternatively, call Crimestoppers on 0800 555 111.