By early Thursday afternoon there was a tailback of 5 km at the southbound entrance to the tunnel, meaning a waiting time of one hour.
Viasuisse, the national traffic information service, warned that the tailback would stretch to 12 km later on Thursday with a waiting time of two hours to enter the tunnel, 20 Minuten reported.
It said traffic had begun to back up at around 7am.
The situation is expected to ease up overnight before the peak is reached on Friday between 7am and 3pm.
From 6pm on Friday there are not expected to be major delays.
There are no reported delays on alternative routes to the south.
Viasuisse recommended the San Bernardino route, particularly for motorists from northwestern Switzerland, Zurich and eastern Switzerland.
The Blick newspaper advised holidaymakers to avoid the queues by staying at home.
According to meteorologists quoted by the paper the whole country is in for mixed weather over the weekend, with rain in Ticino on Sunday.
“Sun, rain and cold wind – everything is possible,” said Roger Perret of Meteonews.
Only Saturday is expected to see really good weather, he said, advising skiers to choose that day to head to the slopes.