The sickening attacks are believed to have been carried out by the killers hiding and luring the animals to them.
A Cleveland Police spokeswoman said: "The people responsible for these sickening and cruel acts appear to have hidden in bushes and lured the sheep to their deaths."
Two youths - aged 14 to 16 - were seen on the farm, carrying air weapons in the weeks prior to the incidents.
* Call PC Stewart Longstaff on 01429 8616768 with any information.