The Health and Safety Executive is investigating high levels of stress-related illness among staff at Wolverhampton University.
Leaders of Natfhe, the lecturers' union, and Unison, the union for administrators and support staff, are meeting HSE officials over the next week to discuss the problem.
It is understood that local GPs have been alerted by unusually high numbers of university staff asking for sick notes as a result of stress at work. The HSE visited the university two weeks ago to investigate the issue with management and key staff.
Union leaders say the university's "bullying" style of management is to blame. Simeon Greene, Unison branch officer, claimed staff had been subjected to "diabolical decisions and actions", including the threat of redundancies.
He said: "I believe one of the biggest problems is bullying managers. They are under pressure to deliver and so they go around kicking everyone. It seems to be getting worse rather than better.
"So far the managers' response to complaints about stress has been that a certain amount of stress is good for you. We are hoping that the HSE will issue an enforcement notice to take the issue seriously and address it."
But the university said it considered stress a serious issue and was conducting research in collaboration with other institutions to discover its causes.
Tom Wilson, head of Natfhe's universities department, said there was no question the problem of stress was getting worse across the sector. Surveys in other institutions had shown as much as half of staff were suffering from stress symptoms, including anxiety attacks.
"I am very glad that the HSE is getting involved, because clearly this is a big issue," he said.
A university spokesman said: "Stress at work is an issue that is raised by staff representatives and the university takes it very seriously. As with other universities, we face increasing pressures from the government to teach and research more cost-effectively and this puts pressure on all staff.
"We are involved in a joint project with a number of other universities to better understand the impact of stress in higher education. In the meantime, we have strengthened our occupational health team to be able to better support staff with stress."