The "unseasonably cold, wet and windy" weather will continue over the next week, according to Met Eireann. It may also continue to disrupt flights and ferry crossings. Driving conditions will remain treacherous at times, according to AA Roadwatch.
Mr John Doyle, of Met Eireann, described weather over the bank holiday weekend as "very unpleasant".
Munster had the worst of the heavy rain, with flooding in parts, while predominantly westerly winds made an already cold few days feel even colder.
"Temperatures have been about two degrees below average for this time of year. We've been seeing temperatures of about 8 to 10 degrees when normally they'd be about 10 to 13 degrees," he said.
It will continue to be colder than usual throughout the week.
"The outlook overall is for cool, breezy and showery weather," said Mr Doyle.
The north and west would bear the brunt of the bad weather, being more exposed, while showers would become isolated in the east and south. The south and east, however, could expect colder nights with a higher risk of frost.
Heavy rain made driving conditions treacherous, particularly in the south, west and midlands, according to AA Roadwatch.
"Visibility has been awful, with three days of constant rain," Ms Ivanna Lyons said. The main effect had been to slow traffic. Yesterday evening there were tailbacks of nine miles between Moate and Athlone and one of five miles into Enfield.
Although things have been bad here they have been worse in Britain where weather has delayed flights in and out of London, Manchester and Birmingham. About 310 flights in and out of Dublin Airport - out of a total of 444 - were affected by weather yesterday, according to a spokeswoman for Aer Rianta.
Some 15 flights in or out of Cork were delayed and about nine in or out of Shannon were affected, she added.
Ferry companies had expected the disruption to timetables caused by stormy conditions over the weekend to continue yesterday.
However, although it had cancelled some fast ferry sailings from Dublin to Holyhead at the weekend, Stena Line's four sailings left as scheduled yesterday. Irish Ferries cancelled five sailings over the weekend, as well as two yesterday.
Intending passengers should contact Irish Ferries at (01) 6610715, Stena Line at (01) 2047777, Swansea-Cork Ferries at (021) 4271166, Dublin Airport at (01) 8141111 for up-to-date information.
Ryanair will put on extra flights today for hundreds of passengers stranded at Beauvais airport outside Paris yesterday. A company spokeswoman said last night that three flights from Paris and three from Gatwick could not operate because of "freak weather conditions" which closed all northern French airports and severely disrupted airports in southern England.
Asked whether passengers had been offered overnight accommodation or food, the spokeswoman pointed out that it was normal policy to offer a booking on an alternate flight or a refund of the ticket price.
She could not comment on reports that passengers were told they could not be guaranteed flights home until November 7th.
