Met Eireann has issued a 32-hour wind warning which will be in place for every county.
The nationwide Status Yellow alert kicked into place at 3pm on Saturday, and it will be valid until 11pm on Sunday night.
The national forecaster sent out the alert as gusts of up to 110km/h are expected to hit.
Places on hills and coasts will be worst affected - while there will also be a risk of flooding.
Meanwhile, nine of those counties will be under a Status Orange warning between 10am and 10pm on Sunday.
The caution for Donegal, Galway, Leitrim, Mayo, Sligo, Clare, Cork, Kerry and Limerick was issued as gusts as strong as 120km/h are being forecast.
A Met Eireann weather warning said: "Southwest winds with mean speeds of 60 to 80 km/h with severe gusts of up to 120km/h, strongest on exposed hills and coasts, with a risk of coastal flooding."
A forecaster added: "The effects of Storm Dennis will continue on Sunday.
"A very windy day with stormy conditions in Atlantic coastal counties. Sunshine and widespread heavy squally showers, especially in the north and west, with a risk of hail and thunder.
"Some of the showers may turn wintry on higher ground. Highest temperatures of 7 to 9 degrees, but feeling colder in strong to gale force southwest winds, with severe and damaging gusts."
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