Two ponies had their tails cut off below the bone in Hebden Bridge.
The incident happened overnight last Friday at Higher Blackshaw Farm, Blackshaw Head.
While the tales were cut below the bone, meaning the animals were not left bleeding, the loss of the tails will have left the animals in discomfort.
PC Fiona Igo of the Upper Valley NPT, said: “We are appealing for witnesses or information about this unpleasant incident which has understandably caused distress to the animals’ owner.
“The loss of the tails will cause the animals distress as horses use them to swat away flies and insects.
“Officers are investigating whether the tails may have been cut off to sell on and we would ask anyone who has information to contact us on on 101 or CrimeStoppers on 0800 555 111.”