Almost 5,000 homes are now without power throughout the country this morning.
Galway, Sligo, Wicklow, Cork, Dublin, Donegal and Waterford have all been hit.
Network crews are also dealing with outages in Kerry, parts of the midlands, Wexford and Wicklow.
Faults overnight due again to the bad weather. To check if a fault in your area or any updates check http://t.co/lqL3Bu8pNl— ESB Networks (@ESBNetworks) January 3, 2014
ESB Networks said crews have been out since first light assessing damage to power lines, particularly in the mid west and north west of the country.
The worst affected areas are in Galway, where more than 1,500 customers have no electricity.
In the Ballyshannon area of Donegal, 380 homes and businesses are without supply.
“The electricity network resiliently withstood the wind and rain it was subjected to by the storm of last night,” said a spokesman.
“This morning any damage caused will be assessed and repaired under normal ESB Networks business operations.”
WICKLOW: The Baltinglass/Ballitore Rd (R747) has reopened just outside Baltinglass following the removal of a fallen ESB wire.— AA Roadwatch (@aaroadwatch) January 3, 2014
Evelyn Cusack of Met Éireann says the intense rain and wind will continue through the morning.
"We've had gusts of us to violent storm-force 11, and that's gusts in excess of 130kph," she said.
"So it's at its most intense now and for another two hours swiping through the north-west."
Staying extremely wind in the west & north.More heavy showers also,some thundery.Highs 6-9C.The winds will slowly ease during the day— Met Éireann (@MetEireann) January 3, 2014