The self-assessment deadline passed at midnight on 31 January.
But many taxpayers could not file their tax returns because of the volume of traffic using the Revenue's website.
The Revenue now says that any failed submissions which are re-sent within 14 days will not be liable to the 100 fine for late payment.
Traffic jam
Nearly 900,000 taxpayers missed the 31 January deadline last year and received an automatic 100 fine as a result.
This year, large numbers of people reported to the BBC that they were having difficulties using the Inland Revenue's online self-assessment filing system.
This was partly because record numbers of people were filing their returns online.
Some taxpayers complained the site was running too slowly to do anything, while others were rejected by the website while submitted their returns.
An estimated 9.5 million people have received self-assessment returns for 2003/04 tax year.
By the end of December, the Revenue had received six million completed returns.