The wet and windy weather of the bank holiday weekend is expected to become less severe in coming days, Met Eireann has said.
The forecast is for cool, breezy and showery weather until the weekend.
"There are no indicators of any severe weather over the next few days," said Mr David Rogers, a forecaster with Met Eireann.
There was heavy rainfall on Saturday and Sunday, but "about 80 per cent of the State is pretty dry at the moment," said Mr Rogers, adding that there had been no serious rainfall since the bank holiday weekend.
After weekend disruptions, Irish Ferries and Stena Sealink said sailings were on schedule again. Aer Rianta said flight schedules had also returned to normal.
Even though the winds are less severe, AA Roadwatch has advised drivers to proceed with caution, paying special care while crossing bridges due to strong crosswinds, and to watch for fallen trees.
The strong winds, which came from the Atlantic and are currently battering England and Wales, did not hit Ireland as badly over the weekend, and they are not expected to be heavy over the next few days.
At the weekend Munster had the worst of the heavy rain, experiencing spot-flooding throughout the region, with predominantly westerly winds lowering the temperature. Flooding also occurred in Waterford.
Flights were disrupted and driving conditions were described by AA Roadwatch as treacherous at times.
The storms centred in England did affect areas in the south of Ireland, with rainfall in excess of one inch recorded in Valentia, an amount described as "fairly exceptional" by Mr Jerry Scully, a Met Eireann forecaster.
Rosslare recorded almost an inch of rain on Monday.
The temperature is currently between 9 and 11, which is lower than normal.
Meanwhile, after an appeal for help from electricity companies, 95 ESB emergency repair crew personnel have arrived in Britain to help fix electricity lines damaged by high winds, leaving thousands of people without power.
Earlier this year ESB crews travelled to France to repair lines.
There is currently a fresh to strong north to north-west airflow over Ireland, which will bring showery weather in the next few days.
Some showers will be heavy or prolonged with a risk of thunder or hail in places.
Towards the end of the week some depressions and fronts are due to arrive, which may bring more bad weather, but it is too early at the moment to determine their effects, said Mr Rogers.
The north and the west will experience the brunt of any bad weather, as they are more exposed. Showers will become more isolated in the east and south.
The south and east, however, could have colder nights with a higher risk of frost.
The Green Party is demanding that the Government acknowledge that the current extreme weather conditions are caused by global warming.