Between Sunday night and Monday morning, a dog, described as a black-faced Alsatian, attacked and killed two sheep at a farm at Wolverley, between Wem and Welshampton.
Six other sheep were injured and had to be destroyed.
There have also been a number of dog problems reported at Whixall where 28 animals had been lost over two months.
Anyone with information should contact police on 101.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org