At the peak of the storm on Wednesday, 260,000 were without electricity for a time.
"It's a mammoth task," Jerry O'Sullivan of energy supplier ESB Networks said.
A number of train, ferry and bus routes were cancelled for a time on Wednesday and Shannon and Cork airports closed temporarily due to gusts of up to 160 kilometres per hour.
A stationary plane at Shannon airport, in the southwest, was blown onto its wing.
What has been described as a mini-tornado caused considerable damage in the western county of Roscommon on yesterday.
Across the country, the winds brought down trees, power lines and the roofs of a number of buildings were blown off.
There are also several reports of cars being crushed by fallen trees.
Neighbouring Britain has suffered widespread flooding after the wettest winter in 250 years and Wales and England were also lashed by storms yesterday.
