Around 60,000 days were lost by Swindon Borough Council to long-term sick leave in one year, a six of which was for "psychological" reasons.
60,000 days were lost between September 2005 and 2006
Figures released under the Freedom of Information Act show that about 500 employees took long-term sick leave between September 2005 and 2006.
Long-term sick leave is defined as being absent for more than 20 days.
Council leader Rod Bluh said a free and confidential counselling service was available to all staff.
But Bob Cretchley, Unison representative for Swindon, blamed constantly shifting work patterns.
He said: "They're under pressure and having jobs and location changed. It is very hard for people to perform adequately in those circumstances."
Mr Bluh said: "We have on-site occupational health service and all stress-related cases are referred there so they can be quickly assessed.
"We want to get people back to work as quickly as possible but if they are stressed and upset, that is not good for anyone."