Galway Bay FM Newsroom - Department of Education Figures have shown that 108 classes in Galway had 30 or more pupils in the last academic year.
The figures, provided to Sinn Fein Education spokesman Donnchadh Ó Laoghaire and published in the Irish Times, showed that than 66,000 primary school pupils were in classes with 30 pupils or more nationally.
This included 208 classes with 30 or more pupils in the Cork County Council area and other areas with high numbers included South Dublin County Council with 142, Meath with 113 and Limerick with 106.
Overall, 2,120 classes had 30 or more pupils last year, with some in Co Monaghan having 39 students and others in the south and west regions having 38.
The Irish National Teachers' Organisation general secretary John Boyle said it was "a crying shame" and a lingering national embarrassment.
Mr Boyle said measures to reduce class sizes should be announced in the budget in order to end "this lingering national embarrassment and provide equal opportunities for Ireland's children with their European counterparts".
The pupil-teacher ratio was due to reach a historic low of 25:1 in the last academic year, though this is still a way off the EU average of 20:1 and about 21:1 in those states who are members of the Organisation for Economic Co-operation and Development.