The Educational Institute of Scotland (EIS) claimed some of its members were now at "breaking point".
Union leaders spoke out on the issue as a new campaign aimed at reducing teachers' workload got under way.
The EIS hopes to reduce "unnecessary" administrative pressures on teaching staff in all school sectors.
Hugh Donnelly, secretary of the EIS Glasgow local association, spoke out on the issue ahead of the campaign's first event taking place in the city tomorrow.
He said: "Glasgow teachers are at breaking point due to increasing workload burdens - stress, burnout and depression are the extreme, if increasingly common, result of workload pressure.
"However, what is more common and more certain is the impact on the learning of children and young people.
"Despite the toxic combination of budget cuts and curricular change, teachers are committed to doing their best by their pupils, but are increasingly feeling the pressure. After years of cuts, there is no fat left to trim."
Teachers are staging a rally in Glasgow tomorrow, which will be addressed by EIS general secretary Larry Flanagan.
Mr Donnelly said schools were suffering as a result of a "retreat to minimum staffing standards" combined with rising pupil numbers and an increase in the number of pupils needing additional support or need needing help with English.
"There are fewer teachers, fewer support staff, a lack of supply cover and less management time to deal with the demands," he said.
"These same pressures do not exist for those, including politicians, who can opt out and buy privileged private education, with the promise of smaller class sizes and specialist support.
"Teachers are doing their best to make sure children are not further disadvantaged due to budget cuts and growing poverty. They are bending over backwards but are reaching breaking point.
"The introduction of a new curriculum, especially tight timetables for the introduction of new qualifications, is being sorely felt.
"The growing bureaucracy associated with the new curriculum has been recognised by the Government.
"We do not wish to be alarmist but there has to be some honest accounting with regard to the challenges being faced by teachers and the impact on the children they teach."