Nearly 15,000 secondary school pupils across the United Kingdom were surveyed for a report published by the British Psychological Society.
It found that more than a fifth had received nasty or aggressive messages from fellow pupils on their phones or computers. In 2002, the figure stood at 14.5 per cent.
The survey also found that girls were more likely than boys to be the victims of so-called "cyber-bullying".
Nathalie Noret, who was part of the research team, said the rapid advance of technology meant bullying was now "moving out of the playground".
"Teachers and parents need to realise that a child's mobile phone or computer isn't just a communications tool - it is also a way for a bully to reach children in their own home," she said.
"Common sense suggests that at home you are safe, so to get that sort of nasty message must be very distressing."
Ms Noret, who is based at York University, said the rising popularity of websites such as MySpace and Bebo, which allow users to leave messages for one another, has provided another avenue for the bullies.
She said: "Parents need to be aware this is happening, and children need to know that if they are receiving these messages they should talk to people.
"Young people are very good at keeping up with the latest technology and have become very adept at setting up their own websites.
"Bullying among girls has always centred more on indirect aggression such as name-calling. Text messaging and the internet are ideal vehicles for that."
Judith Gillespie, of the Scottish Parent Teacher Council, said she was not surprised that girls were the victims of cyber-bullying more often than boys.
She said: "Girl-on-girl bullying is usually psychological rather than physical. But youngsters do have some control over this type of bullying.
"The phone number tells you who a text is from, so they should just delete it without reading it. The same goes for e-mails.
"Once the bully realises that they're not upsetting someone, they tend to stop doing it."
The latest research backs up a separate study published by the children's charity NCH in 2005, which claimed that mobile phone bullying in schools was reaching epidemic proportions.
Three-quarters of teachers surveyed said text bullying had become commonplace, particularly in primary school playgrounds.
The study also found eight out of ten teachers had been approached by a child worried about mobile-phone bullying.
Graham Cooper, a spokesman for NCH, said: "Young people tell us mobile phone bullying has become a real problem.
"It can be easier to intimidate someone by phone than to do so in person."
• A NEW anti-bullying service launched by the Scottish Executive last week said tackling cyber-bullying was one of its key priorities.
The Respectme service has been set up to deal with bullying both inside and outside the school gates.
Hugh Henry, the education minister, said bullying was now more likely to take place outwith the school.
"Today's youngsters also have the potential problems of cyber and text bullying to contend with," he said at the scheme's launch in Glasgow.
Brian Donnelly, the director of Respectme, said yesterday: "The increased use of mobile phones and the development of social networking websites is taking bullying into children and young people's homes and personal spaces - places in which they should feel safe.
"We will work to raise awareness of this cyber-bullying and the responsibilities of the adults who come into contact with children and young people, to ensure that they are safe from bullying in all settings."