Late on Sunday evening, 4.8 million of the 7.6 million Swedes who have to file their income taxes had done so electronically - either online or via SMS.
The Tax Agency (Skatteverket) said it did not have information on how many Swedes had opted to send in the actual paper copy of their tax details.
The agency cautioned against filing taxes at the very last minute, especially if the person has any questions that need to be answered by a call-centre agent.
At 9am on Monday, the agency had 504 agents working to help Swedes grappling with their papers. A call to the help centre was placed in a queue - at number 517 - with an estimated waiting time of nine minutes.
"If you have questions it is important to file your taxes early in the day, so you have time to have those questions answered," spokeswoman Anna Sjöberg told the TT news agency