Five Gaelscoileanna at primary level in Dublin have waiting lists of 100 pupils or more.
A total of 5,000 primary children nationwide will start in junior infants in the Irish-language schools this September, according to a spokeswoman for their representative organisation.
She said that in relation to waiting lists for Gaelscoileanna: "20pc of the schools are over subscribed."
Another school is required on Dublin's southside to meet the demand, she said.
"Different schools have different enrolment policies. For instance, some will only accept names from the November in the year prior to starting. Others will accept names literally from birth," she said.
Of the Gaelscoileanna at primary level in Dublin, five of have waiting lists of 100 or more. One school has 200 on its list. However, this can change for different schools year on year. Overall, there are 144 all-Irish primary schools in the Republic, outside the Gaeltacht regions.
Meanwhile, Luke O'Shaughnessy, the spokesperson for the Educate Together schools, said that some of its schools in Dublin, "receive up to five times the number of children's names than they can actually accommodate with school places each year.
"Given the high demand, families tend to put their children's names on waiting lists very early" he said.
"We've heard anecdotal evidence of parents registering their child's name with the local Educate Together school right after the child's birth," he said.
He said that the "welcome opening of six new Educate Together schools this September will not be enough to meet the rising demand for multi-denominational school places in Ireland, and additional provision is badly needed".
He said that the Department of Education has acknowledged that there is need for an Educate Together primary school in 25 areas around Ireland.
"Educate Together's own evidence from requests to its offices and schools and from public census and survey data would double that figure," he said.
Figures show that there are a total of 3,286 primary schools nationwide aided by the Department of Education, under Minister Jan O'Sullivan.