Gardaí in Cahirciveen are investigating the destruction of a grave of one of the babies at the centre of the Kerry Babies Tribunal.
The baby's body was discovered on a beach near Cahirciveen in March 1984. He had suffered a number of puncture wounds and the post-mortem showed he had been stabbed to death.
Gardaí believe the black marble headstone was vandalised with a heavy instrument like a sledgehammer some time between Sunday night and last night.
No other grave in the cemetery on the Waterville road is understood to have been damaged.
The simple wooden cross that marked the grave for the past 20 years was replaced by marble headstone last February. The baby's grave has been targeted by vandals in the past.
The parents of the baby, given the name John posthumously, and the exact circumstances leading to his death have never been established.
Ms Joanne Hayes, who at the time was a 25-year-old single mother from Abbeydorney in Kerry, was the primary Garda suspect. During the investigation, she was reported to have admitted to killing the baby and was charged with murder.
Members of her family were also charged with concealing the crime. Ms Hayes later retracted her confession.
The body of a second baby was found on the Hayes farm and Ms Hayes said she had given birth to this baby on a field before the baby died. This baby had a different blood type from the baby found on the Cahirciveen beach.
The finding of the second baby's body cast serious doubt on the Garda handling of the case.
In the autumn of 1984, a tribunal of inquiry was set up to look into the handling of the investigation amid claims by the Hayes family that members of their family had been assaulted during questioning.
The tribunal found that Ms Hayes was not the mother of the baby found murdered on the beach and was not responsible for that baby's death. However, Justice Kevin Lynch, who headed the inquiry, concluded that Ms Hayes had killed her own baby by choking it to stop it from crying.
The Lynch report criticised the Gardai's handling of the case but rejected the claims of assault by the Hayes family. He also rejected claims that there had been a police conspiracy in the case.