Around 8,000 homes and businesses are without power on Monday morning.
Storm Floris made landfall overnight, bringing damaging gusts and localised flooding to some parts.
ESB crews are working to restore electricity faults, with Galway, Clare, Mayo and Donegal among the worst-affected counties.
Weather warnings are in place for eight counties as Storm Floris hits the country overnight.
Met Éireann has warned of dangerous travelling conditions, power outages, and structural damage.
A status yellow wind warning is in place for Cavan, Donegal, Leitrim, and Monaghan since 4am until 4pm.
There is also a yellow wind warning for Clare, Galway, Mayo, Sligo, which will last until 1pm.
Met Éireann has warned this could lead to fallen trees, debris and loose objects, dangerous travelling conditions and power outages.
A yellow rain warning is also in place for Donegal, Galway, Leitrim, Mayo, Sligo until 10am on Monday.
Met Éireann warned this could cause localised flooding and lightning damage.