The police and army personel claim that the government did not provide sufficient protection during shooting practise.
Cormac Keenan, a Belfast lawyer, said the hearing problems could have been avoided "because it has been known for a long time that excessive noise causes long term hearing damage."
According to lawyers for the police and army personnel, both in service or retired, soldiers for years had used cigarette butts as ear plugs.
The Irish government was forced to pay 350 million euros (460 million dollars) for a similar compensation claim at the end of the 1990s.