Three new weather warnings have been issued for tomorrow as the clean-up following Storm Éowyn continues.
Two Status Yellow warnings for wind have been issued for six counties, along with Munster, with Met Éireann warning of further damage to already weakened structures and trees.
The first begins at 6am and covers Munster. It is valid until midday.
Then a Status Yellow wind warning will come into place at 9am for Carlow, Dublin, Kilkenny, Wexford, Wicklow and Galway.
Dangerous travelling conditions are possible during the alert, which will end at 3pm.
The second warning will be in operation for Cork, Kerry and Waterford from 11pm tomorrow night until 6am on Monday.
A Status Yellow warning for rain will be in effect from 5am until 5pm tomorrow for Carlow, Kilkenny, Wicklow, Cork, Kerry, Tipperary and Waterford.
The forecaster said that heavy downpours of rain may lead to spot flooding.
Yesterday, Storm Éowyn brought record-breaking gusts of 183km/h, and the damage is still being assessed around the country.
Meteorologist Linda Hughes urged people to take precautions if they have any trees or structures damaged by the as "if structures are weakened, we are going to see more implications".
Around 442,000 farms and businesses across the island of Ireland are still without power.
ESB Networks said around 402,000 customers are without power, while some 140,000 homes and businesses were without electricity in Northern Ireland.
ESB Networks Regional Manager Brian Tapley said the power outages are "unprecedented" in terms of the numbers and "widespread damage to our network".
He said crews at local depots began dealing with "extreme danger calls" from around 6am yesterday and damage assessment unfolded throughout the day.
ESB has warned that it could take a number of days before power is fully restored.
Meanwhile, Uisce Éireann said that more than 120,000 people are without water and warned that supplies for a further 400,000 people were at risk.
A total of 235 flights were cancelled at Dublin Airport while structures, including a multimillion-euro indoor playing facility in Co Mayo, were severely damaged during the storm.
Northern Ireland's Department of Infrastructure said more than 1,800 objects had blocked roads, and that teams would work to clear them once weather alerts had lifted.
Financial support will be available for families and businesses - Housing Minister
Minister for Housing, James Browne has said that financial support will be made available to families and businesses affected by Storm Éowyn.
"It is a whole Government approach to see what supports are needed for those businesses and for those families who have been affected," he said.
"Supports will be put in place.
"What exactly they are will be assessed over the coming days and get them out as quickly as possible."
Mr Browne urged people to exercise caution over the coming days as many structures are still unsafe.
"We have some yellow wind warnings coming in...They are going to be a little bit more dangerous than normal for yellow warnings."
He said that "every effort" is being made to restore power to homes "as quickly as possible."
