One lamb died after being attacked at a farm in Denby Dale and another was seriously hurt. Both had claw-marks that looked like large, feline paws.
One theory is that the beast could be a lynx which has escaped from a nature reserve. But experts urged caution - saying it could be a large domestic cat living in the wild.
Several people are said to have spotted a powerful black beast roaming around Denby Dale.
Farmer Mr Richard Wood had two lambs ripped apart and another is missing, presumed eaten.
One witness, who saw the animal try to pounce on bantam hens, said it was a large animal, with a head as big as a human head.
Mr Wood, of Perch House Farm, Denby Dale, said: "There have been a lot of sightings, dating back to August.
"One man said his dog came across the big cat in some bushes. Another saw it go for bantams in his garden.
"It's been spotted at Bagden Hall, Scissett, around Skelmanthorpe cemetery and in High Hoyland."
Tim Coy, Huddersfield group secretary of the National Farmers' Union, said the animal was probably just a large domestic cat which had turned wild.
"Farmers are bound to be worried. The only precaution is to move lambs closer to their farms," he added.
Denby Dale vet Tony McCarthy, who examined injured lambs, said: "We have not come to any conclusion about the injuries - but to say it is a wild animal is a bit far-fetched."
Pc Steve Downing, West Yorkshire police wildlife officer, said: "This is the first time people in this area have complained of their sheep being injured by a big cat."
He said there were no wildlife parks in West Yorkshire or north Derbyshire from which a lynx or wild cat could have escaped.
"I would urge people not to be concerned, because if a large cat had been roaming about for weeks we would have heard of more animals being injured," he added.
Yorkshire ABC Savages Denby Dale Sheep
A mysterious and powerful black animal is being blamed for sheep savaging. [Original headline: Mystery Over Big Black Cat]
Anyone who thinks they have seen the animal should phone Pc Downing on 01422 318010.
Huddersfield Daily Examiner / Yorkshire | By Jenny Parkin & Karen Grattage - June 23 2000
