The ESB is advising any customers experiencing a loss of supply to check their website for updates.
It follows high winds and lightning strikes yesterday, which have left thousands of homes without power.
Crews restored electricity to over 30,000 homes and businesses across Ireland on Christmas Eve.
However, efforts to restore power to some homes on Achill Island in county Mayo got underway earlier this morning.
People on the island are being advised to conserve power and customers can also check their website at www.esbpowercheck.ie