Maharishi Mahesh Yogi became a well known figure in the 1960s
Cardiff schools could introduce a pilot Transcendental Meditation (TM) programme to relieve stress on pupils.
One unnamed secondary school is to give it a trial on a voluntary basis.
It followers say TM is a means of clearing and resting the mind through a series of chants and relaxation exercises which anyone can learn.
Freda Salway, Cardiff council's executive member for education, said anything to lessen the load was a welcome addition to the curriculum.
TM hit the headlines in 1967 in Wales, when the Beatles met the movement's founder Maharishi Mahesh Yogi on a retreat in Bangor.
According to south Wales instructor Helen Evans, however, the 60s left a legacy of mixed blessings, with TM becoming more widely known and associated with the era of psychedelia and the Woodstock generation.
"Sgt Pepper and the like probably put back serious scientific research into the benefits of TM by about 10 or 20 years," said Ms Evans.
"But experiments in US schools have found that it can have a dramatic effect on reducing violence and bullying in the classroom, as well as improving concentration and self-esteem."
Ms Evans said: "Most meditation systems will tell you to blank your thoughts out, but I don't think that's realistic. As soon as someone tells you to think of nothing, then something will pop into your mind.
Proponents believe TM makes you a more relaxed and contented person
"The thing that's different about TM is that it teaches you to cope with the feelings that you do have rather than trying to get rid of them.
"It's about relaxing, giving your mind the space to rest and allowing your subconscious to come to terms with problems without the clutter that's normally there."
She said modern life could be "highly stressful because there's so much about our lives which we can't control ourselves". She added: "If you can find a way, not of changing your emotions, but of coping with them and accepting them for what they are, then you can be a much more relaxed and contented person with better self-esteem".
Ms Salway said: "It's not going to work for everyone, but it's certainly not going to do any harm.
"Like anything, you can't ram it down people's throats - it's entirely up to students and their parents to decide if it's something they'd like to try.
"But today's children face more stress than any generation before them with exams and peer-pressure and problems in the home.
"So if TM can provide an outlet for even a small percentage of them, then it's something worth offering."
Several schools in England are already in the process of introducing TM to staff and pupils, with funding from a foundation set up by cult film director David Lynch.
A common objection from parents, especially in highly multi-cultural areas, has apparently been a perception that TM is closely associated with Buddhism and Hinduism, and is therefore incompatible with other faiths.
But north Wales instructor David Hughes said TM had a strictly non-denominational approach.
"Yes, TM has its roots in India, and there are some overlapping features with Buddhism and Hinduism, but fundamentally it's a technique, not a belief system," he said.
"It's practiced by millions of Muslims, especially in the Middle East, and it's no more true to say that TM is Buddhist than it is to say that singing is Christian."
"It's something which comes naturally to some people - elite athletes like Usain Bolt seem to slip into the zone without ever having been taught.
"But most people need a little bit of help to harness the mental powers we all have inside."
If the pilot study is a success, it could be offered to students throughout Cardiff.