Irish Rail says up to 400,000 journeys will be made on Intercity trains during the Christmas period.
With Christmas Eve falling on Monday, Irish Rail expects an even spread of passengers over the weekend.
There are no rail services on Christmas Day or St Stephen's Day.
There will be changed timetables over Christmas, so Irish Rail is advising people to check timetables before travelling.
More than 620,000 passengers are expected to pass through Dublin Airport during the festive period.
Elsewhere, heavy rain caused misery for rail passengers in many parts of Britain, while homes and businesses in southwest England were hit by flooding.
Motorists and shoppers also faced difficult conditions on one of the busiest weekends of the year for travel and shopping.
Four severe flood warnings, which means there is a danger to life, were issued in Devon and Cornwall.
The town of Braunton in north Devon was effectively cut off, with homes and shops under water, after the River Caen burst its banks.
The Environment Agency (EA) said there was a heightened flood risk across Cornwall, Devon, Somerset, Dorset, Bristol, Hampshire, the Isle of Wight, West and East Sussex, North Yorkshire, South Wales, Ceredigion and Gwynedd.
Many people had their Christmas travel arrangements disrupted as rail services were badly hit.
The First Great Western train company advised passengers whose travel was not essential to avoid any journeys west of Taunton in Somerset because of flooding and landslips.
Arriva Trains Wales told passengers to avoid any rail travel in South Wales.
Both operators were using road vehicles to transport passengers, but efforts were hampered by a lack of vehicles and flooded roads.
East Midlands Trains suspended services between Derby and Nottingham because of flooding, while there were no trains between Stirling and Perth.
The Highways Agency said there were a handful of flooding incidents affecting roads, including the closure of the A21 in both directions near Battle, East Sussex.
In Scotland, 17 flood warnings - mostly in Tayside - and 15 flood warnings were issued by the Scottish Environment Protection Agency.
The Met Office released amber weather warnings, which mean "be prepared", for heavy rain and strong winds across southwest England, Yorkshire and Humber, Wales, central Scotland and the Grampians until tomorrow morning.
Busy weekend for retailers
Meanwhile, Irish retailers are expecting this weekend to be one of the busiest shopping weekends of the past five years.
With huge numbers doing their Christmas shopping today, Retail Excellence Ireland said traders can move into 2013 with optimism.
Spokesman David Fitzsimons said there were several reasons for today to be busy.
He said: "The weather is clement and people have postponed spending because they were waiting to get the Budget out of the way.
"A lot of people have taken Monday off, so it is kind of like a long weekend, and a lot of people have just left their shopping late.
"We are seeing huge footfall down from Belfast because of the exchange rate and also because of some of the trouble up there.
"People got paid this week, so all the signs are good for a very, very busy and productive retail day today."