The animals worth thousands of pounds went missing from Lendalfoot fields, six miles from Girvan, between May 25 and June 10.
The woolly creatures — called Cross Mule Ewe Hoggs — have orange tags and blue marks.
PC Jamie Dunlop said: “We are appealing to anyone who has seen anything suspicious in the area to come forward.
“We urge people to be vigilant.” “If anyone needs advice on rural security please contact 101.”
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