Met Éireann has issued a Status Yellow rainfall warning for Munster and Connacht, along with counties Carlow, Kilkenny and Wexford.
Some river and localised surface flooding is possible, with rainfall totals of 30 to 50mm, highest in mountainous regions.
Weather for the days ahead
Today will remain breezy, with sunny spells and scattered showers. The showers will be heaviest and most frequent in Atlantic coastal counties, but staying mostly dry in the east of the country.
Tonight will be mainly dry apart from a few showers in west Munster and west Connacht. It will become quite cold with a risk of frost, with lowest temperatures of 0° to 4°.
On Monday night, it will turn increasingly windy with south to southeast gales developing on coasts. Rain will develop in the southwest and west early in the night, before extending nationwide after midnight.
It looks set to be a wet and very windy day on Tuesday, with further spells of heavy rain pushing northwards over the country, accompanied by strong to gale force southerly winds.
Many areas will be dry on Wednesday night with some clear spells, but a few showers will continue to affect parts of west Munster, Connacht and west Ulster.