Mr Drennan said one IRHA member has had a trailer waiting to clear customs since 17 January because inspectors were “too busy” to process it.
He said the delays were having an impact “across the board” on supplies of component parts, agriculture and fisheries as well as retail and parcel delivery.
Hauliers are due to meet with the government later this week to try to overcome the difficulties.
Revenue said on Monday that 79pc of imports are being cleared through customs at Dublin Port without requiring extra checks.
A further 15pc of goods required documentation checks and 6pc were also subject to physical or veterinary checks.
SOME food has been dumped due to Brexit red tape at borders, an Oireachtas Committee heard this afternoon.
The president of the Irish Road Haulage Association (IHRA) Eugene Drennan has called for independent oversight of a review of border systems and checks.
Speaking at a Joint Committee on Transport and Communications Networks, Mr Drennan said that the paperwork required by hauliers at the beginning caused some trucks to be turned away, hence food expiring and having to be dumped.
“A lot of the product that comes through agriculture is repetitive. It’s the same product tomorrow as today,” said Mr Drennan.
The Irish Road Hauliers Association (IRHA) has criticised the “excessive and unrelenting regulatory zeal” of authorities at Irish ports which they say will bring trade to a “complete stand still” and result in significant employment.