More than 25,000 bench warrants have been outstanding for over a year.
The Gardaí have been unable to track down people who are trying to avoid going to court.
Bench warrants are issued by a judge, authorising the Gardaí to arrest a person and bring them before the courts.
They are normally issued after a person fails to appear in court accused of a crime.
One bench warrant Dublin has been outstanding for 52 years, while one in Co Clare has been outstanding for 29 years.
New figures show nearly 34,000 bench warrants are currently outstanding in Ireland.
Almost 25,500 have been in existence for more than a year - with 68% in the Dublin region.
Retired sergeant John Hynes says there are many reasons why offenders may not have been tracked down.
"The main reason I suppose is that people leave the address at which they were residing at the time of the arrest.
"It may be genuinely for work reasons, or just that they don't want to be found if they're prolific offenders and things like that.
"I've found from past experience that Gardaí get very, very little cooperation from families and people who might know where these people are".
Justice Minister Helen McEntee says the execution of bench warrants is a long-standing issue for many police forces.
She says the Gardaí give priority to warrants relating to serious crime.