An extra £1bn has been provided to the NHS for mental health services, but May said she wanted to tackle the problem in a wider sense.
Under the plans, mental health training for teachers and staff will be rolled out to a third of secondary schools in England next year, with the remaining two-thirds of secondary schools offered the support in the following two years.
'Yet left unaddressed, it destroys lives, it separates people from each other and deepens the divisions within our society.
Children and young people's mental health care has been a Cinderella service in the NHS for years, always at the back of the queue for resources and the front of the queue for cuts.
While Rehana Azam, GMB National Secretary, said: 'More than 12% of mental health staff have left and nearly 5,000 mental health beds have been cut since 2010, ' GMB National Secretary Rehana Azam says.
Mrs May will say support for mental health sufferers should be offered not just in hospitals "but in our classrooms, at work and in our communities".
As part of her vision for a "shared society", May will announce measures aimed at improving the support available for people with mental health problems.
Theresa May said the importance of support networks for people with mental illness had been brought home to her by the observation that anyone at work with their arm in a plaster would have colleagues talking about their injury, while "if you have a mental health problem, people are more likely to try to avoid you".
The focus on schools is driven by figures showing over half of mental health problems start by the age of 14 and 75 per cent by 18.
Teachers will be taught how to spot problems such as depression anxiety and eating disorders
"Actually if we look at the issue of mental health in this country, I think it's more about the stigma that still attaches to mental health". School budgets are being cut by £3bn so it will become increasingly hard to fund in-school care for children unless these cuts are reversed immediately.
Paul Farmer, chief executive of Mind, the mental health charity, said it was good that the Prime Minister was talking about mental health.
Today's package has a strong emphasis on early intervention in schools, where problems such as cyber-bullying, "sexting" and eating disorders have added to anxiety about exams to place youngsters under intense pressure.
But Liberal Democrat Norman Lamb, a former health minister, said Mrs May was announcing policies already agreed under the coalition government and called it "a puny response" to "cover up for this government's failure" on delivering.
The Prime Minister says that mental health is one of the areas in which "the power of government" can be used to better people's lives.
"Mental health should be at the heart of government, and at the heart of society and communities - it's been on the periphery for far too long".
"This starts with ensuring that children and young people get the help and support they need and deserve - because we know that mental illness too often starts in childhood and that when left untreated, can blight lives, and become entrenched".
"Much of the additional £1.4 billion of funding secured for child mental health care is being diverted to prop up other services".