The problem is not confined to Scotland’s biggest city and is directly linked to a significant cut in wages for supply staff, it argues.
“The situation is the worst seen for a number of years. Local and national action is needed,” said Hugh Donnelly, Glasgow Local Association Secretary.
The approach of Standard and Higher exams this summer made the problem more urgent.
“Teachers and managers are going above and beyond to meet the needs of young people. Our members, including heads and deputes, are making significant efforts to cope with the shortage of supply cover and rearrange timetables.”
The EIS is in constant dialogue with Glasgow City Council over the problem, which is prevalent in primary as well as secondary schools, Mr Donnelly said. In primaries, headteachers and deputies were often standing in for regular classroom staff themselves.
One member of the union cited a class that had been taught by 29 teachers this academic year owing to subject shortage, while another school was three biology teachers short at one point.
Supply teachers earn just £78 a day before tax, compared with about £150 before new working arrangements introduced in 2011.
“There is little doubt that there is a link between short term supply problems and pay and conditions, and the impact of the reduced rates for short-term supply teaching.”
A spokesman for Glasgow City Council said: “We share the concerns of the EIS about the shortage of supply teachers. This is a national issue and Glasgow has been affected equally with other local authorities.”
A Scottish government spokesman said the employment of teachers, including supply staff, was a matter for local authorities.
“The Scottish Negotiating Committee for Teachers is currently monitoring supply issues and we will play our part in those discussions. The numbers of teachers trained each year includes an allowance to ensure there is a pool of supply teachers from which schools can draw as necessary.”
Mr Donnelly added it was vital to look at the reduction of supply pay, the training and recruitment of teachers nationally, and ways to engage retired teachers who would normally be available to take up the slack of short-term absence.