A confidential hotline and support group have been set up to help the city's 185 heads cope with the pressures of shrinking resources and an increased workload.
The education funding crisis, inspections, national curriculum, larger class sizes and the parents' charter have all been repeatedly identified as causes of stress.
Headteachers, personnel officers and occupational health nurses, have formed a working group on stress management with backing from the city council's occupational health department.
David Hutton, head of Arbourthorne Junior School and a member of the support group, said: "Heads spend most of their time picking up the pieces and dealing with minor issues. At the end of it all they wonder what they have achieved.
"So they work harder to catch up with the important jobs and then they're on a downward spiral."
Since the project started in July primary heads have been briefed on the danger signs of stress, including forgetfulness, touchiness, tiredness, introverted behaviour and aches and pains. For severe stress, such as clinical depression, headteachers can be referred to a counsellor or psychologist.
A similar briefing session will be held for secondary and special school heads this term, so they can help other staff by spotting symptoms of stress early on.
Members of a headteacher mentoring group, which has existed for five years to support newly appointed colleagues on administrative aspects of the job, suggested the project. They were concerned about the number of vacant headships and the proportion of heads leaving their jobs because of stress-related illness.
Joan Fallows, head of Broomhall Nursery, said: "We all knew at least one person who had suffered difficulties and we were concerned that it was often some of the most experienced headteachers."