Hundreds of people had been combing the Borris-in-Ossory area since the 20-year-old disappeared last Thursday.
The body was discovered late yesterday evening.
The remains have yet to be formerly identified, but gardaí say the search for Mr. Finan has been suspended.
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A post mortem examination is expected to take place today.
Borris-in-Ossory Parish Priest Fr Jackie Robinson has been speaking to Midlands 103.
He says Shane Finan was a much loved young man: