Girls were particularly concerned about their appearance, with 16% of them saying they had been picked on because of how they looked.
A SHEU spokesman said it was unacceptable that so many kids were being targeted by bullies.
"It's not about shoving and name-calling. It's often more subtle," he said.
The study also threw up some other interesting statistics.
For example, the number of boys reading in their spare time dropped from 29% to 17% between 1997 and 2002.