Carlow and Kilkenny will have a yellow wind warning in effect on Wednesday with the threat level for County Donegal set at orange.
Storm Dudley is expected to bring damaging gusts of up to 130 kilometres per hour to the North of the island and up to 110km/h locally.
It could be even stronger on high ground and on exposed coasts with some coastal flooding expected.
Clare, Donegal, Mayo and Galway will see a yellow wind warning kicking in at midday for 24 hours.
A yellow alert for the whole country is for 24 hours from midday on Wednesday to 12pm on Thursday.