The event is an annual tournament where students from rival universities compete in various sports over a number of weeks and the finale is taking place this evening at Ice Sheffield.
Sheffield Supertram tweeted that there are delays due to the high volume of people using the trams.
The organisation said: “We are still experiencing heavy delays on the yellow route service due to the high number of passengers boarding.
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“Apologies if you have been affected.”
A customer replied and called for Stagecoach Supertram to “re-think for next year because the journey home tonight didn’t feel safe.”
They added that “letting that many (people) on one tram was equally appalling.”
The organisation tweeted that extra trams have been put on for the event and thanked customers for their patience.
In a statement, they added: “We had extensive plans in place for this event and actually ran 12 extra services before the event.
“We also have a number of extra services planned to get people home after the event.”