The Texel hogs were taken from fields around Awhirk farm, Stranraer.
It happened sometime between September 30 and October 25.
The sheep have either a red or orange shoulder with white faces.
Appealing for public help, PC Elinor Sneddon said: “We want to hear from anyone who may have seen anything suspicious in the area around the B7042 road between Portpatrick and Sandhead over this period, or indeed any other rural location in the Stranraer area.
“A vehicle must have been used and we are keen to hear about any suspicious vehicle movements over this time.”
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