Maximiliano Pereyra and Ariel Diaz, who were jailed for robbery offences, dressed up as the animals after escaping from a maximum security jail in Argentina more than a week ago.
Pereyra, 25, and Diaz, 28, dressed in full sheepskin fleeces with realistic looking heads as they tried to evade capture, The Sun reported.
They had stolen the sheep hides from a local ranch, it was claimed.
They used their disguises to fool officials for more than a week despite more than 300 members of the local constabulary searching for them.
The local police have been left embarrassed by the episode after locals reported seeing the pair running through local fields at night.
"They were wearing grey clothes but had full sheepskins, including the sheeps' heads, over their heads and backs,” said a farmworker at La Almeda.
Details of what the prisoners were behind bars remain unclear.
Police sources said it appeared that identifying the pair among thousands of other sheep was "almost impossible".
"They can't pull the wool over our eyes forever,” one officer deadpanned.