Around 7,000 customers ares still without power following Storm Atiyah, it's understood.
An estimated 12,000 homes and businesses had no electricity on Sunday night, while it's believed 27,000 ESB customers were affected during the height of the storm.
ESB Networks said crews are working to restore faults as quickly as possible.
The company was working on faults in Ratoath, Co Meath and in parts of Co Westmeath on Monday morning.
There are more than 330 properties without electricity in Bushfield, Co Westmeath.
Over 250 customers are affected by power outages at Loughtagalla, Co Tipperary and 238 homes are affected in Inch, Co Kerry.
Winds caused by the storm wreaked havoc in parts of the country as status orange and red wind warnings were issued.
And AA Roadwatch have reported several fallen trees on road across Ireland on Monday morning.
Motorists have been advised to take extra caution due to the conditions caused by Storm Atiyah.
A spokesman said: "There’s wind-blown debris on the roads in a number of areas this morning following Storm Atiyah overnight.
"Take extra caution, especially on secondary routes, and give extra space to other road users."
