The animals were abandoned just outside Edenderry.
Offaly County Council is investigating the illegal dumping of two dead sheep on a greenway.
The animals were dumped near Cartland Bridge in Monasteroris, close to Edenderry.
The local authority says the incident is "extremely distressing" and is the third case of animal remains being dumped at the same location.
The sheep had no ID tags, and Offaly County Council is asking anyone who may have seen suspicious activity to contact them.
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