The theft, between Sunday April 21 and Sunday April 28, was from a property at Waimumu, southwest of Gore.
The stock are valued at $65,000 and police say the rams have distinctive orange spray marks on their backs.
Anyone who might have seen something suspicious in the area or who has information that might assist can contact Constable Wayne McClelland at Mataura Police on 03 203 8164 or information can be passed on anonymously via Crimestoppers on 0800 555 111.
