One in three calls about bullying to a confidential parents' helpline related to teachers and principals intimidating children.
In some cases, according to the National Parents Council (primary), bullying of children by teachers was so serious that parents were left with no option but to remove their children from school.
Of the 552 calls made to the helpline between October and December of last year, 166 were specifically about bullying in schools, and 56 of these were about intimidating treatment of children by school authorities.
In many instances, parents also said that when they raised their concerns with schools, they were informed there was no problem in the school.
Boards of management, they were told, were happy they had investigated the bullying and had found no grounds for complaint.
Ms Fionnuala Kilfeather, chief executive of the primary parents association, said there was an urgent need for the existence of a culture of bullying in some schools to be acknowledged.
"There is no use saying a school has a Christian ethos if the practice in the school doesn't mirror it," she said. "The culture of the school has to be such that there is a culture of mutual respect. It is an easy thing to say, but how to do it is another matter.
"There are some schools that have very little bullying going on, and others that have a lot," she said. "We need to look at what is it in these schools that causes this."
In the case of teacher bullying, she said, parents reported children being "picked on", being called names like "thick" and "stupid", and being made to stand for prolonged periods of time. There were also, she said, a small number of reports of physical action towards children.
"Many schools were reported as having no proper code of conduct or anti-bullying strategy in place," she said. "It's not enough just to develop a policy on this. People are going to need more help, they need to know the how as well as the what."
"It is clear that some school communities have a lot of work to do.
"The culture in the school needs to be led from the top with adults showing by their own example how children should behave."