ESB have restored power to 30,000 homes so far today, with 40,000 still experiencing power cuts.
In the North, around 3,600 customers have been left without electricity.
Winds have caused extensive damage to the electricity network as a result of flying debris, fallen trees and broken poles.
While the damage is concentrated mainly in the south and west, there are customers without supply throughout the country.
Mike Fitzgerald of ESB Networks says the winds are hampering repairs.
ESB Networks worked through the night to repair damage caused to electric lines, but thousands of homes were still without power.
Met Eireann’s red alert warning is in place in south and eastern parts of the country, with Wexford, Galway, Mayo, Clare, Cork, Kerry and Waterford getting the worst of the stormy weather.
The forecaster warned gales of up to 150 kmph are expected to ravage coastal areas and there is a danger that high seas could cause coastal flooding.
Damaging gusts of between 120kmph and 140kmph could batter the worst affected areas.
A less severe orange weather alert is in place for the rest of the country, with particularly high seas in the northwest.
Meanwhile, Irish Farmers' Association president John Bryan urged farming families to take care while working during the stormy weather.
He warned that the dangers during stormy conditions multiply around farmyards, with older and younger family members most at risk of being injured from falling debris or swinging gates.
Mr Bryan added that power cuts on farms increase the work pressure, but said he appreciated that repair crews were on the job.