Up to one in five pupils may be bullied each term, researchers from Strathclyde University say.
Surveys show that anywhere between 6 per cent and 28 per cent of pupils admit to intimidation, while 3-17 per cent say they have bullied others.
Pupils estimate that 7-19 per cent of their school mates are victims and 8-18 per cent are bullies.
Jim Boyle, a psychology lecturer, said the findings were remarkably consistent and showed that bullying happens at all stages and probably in all schools. The peak is among 11-year-olds.
Young people were concerned about it. Bullying was related to under-achievement, truancy and depression and was a factor in two to three cases of suicide each year. Problems may persist into adulthood. But studies had also shown that intervention can markedly reduce its incidence.
In primaries, Mr Boyle said, bullying was most likely to take place in the playground and in secondaries, corridors and classrooms were places of risk. Boys report more bullying than girls.
"Who gets bullied? It is children who are anxious, insecure, lacking in self-confidence and self-esteem," Mr Boyle said. "Children with physical difficulties, or with unusual names or accents. Children with ASNs (additional support needs) in mainstream schools. Children from ethnic minorities or other countries and children new to the school."
Twenty years ago it was common to work with the victim and the bully. Now it is seen as a group problem. "It is a complex social process involving the whole peer group in distinctive roles. No-one in the peer group is unaware bullying is going on and approaches to intervention have to reflect this complexity," Mr Boyle said.
Susie Turner, a psychologist with Falkirk Council, said that work with S1-S3 pupils in one secondary that recognised it had a problem with aggression had shown that bullying could be reduced. Pupils were alerted to the extent of the problem, taught about group influences and the role of the peer group, and shown how to be assertive.
A series of four lessons helped to raise confidence to intervene and to tell someone about it. But Ms Turner said more work was needed on general assertiveness training to bolster the role of bystanders. Older pupils may also benefit from peer support.