The status yellow warning is valid for Dublin, Carlow, Kilkenny, Wexford, Wicklow, Cork, Kerry and Waterford
A yellow rainfall warning has been issued for Munster and Leinster.
It began at 9am this morning, an is valid until 7pm this evening.
Dublin, Carlow, Kilkenny, Wexford, Wicklow, Cork, Kerry and Waterford are likely to be worst affected, with an extra 15 to 25 mm of rain - expected to be heaviest on high ground.
Met Éireann forecaster Pat Clarke says it has been a pretty wet Christmas in general, following on from a month that has seen plenty of rainfall.
Meanwhile ESB says it is increasing the flow of water being released through Parteen Weir due to rising levels on the River Shannon and Lough Derg.
It follows heavy rainfall over the past number of days in the Shannon catchment area.
The flow is being increased to 370 cubic metres per second.
ESB is warning that this may result in flooding to areas downstream including the areas of Springfield, Montpelier, Castleconnell, Annacotty and the University of Limerick.
It comes as more than 200 flood alerts and warnings are in place in England, Scotland and Wales as storm Eva makes it way across the UK.
Rare red flood warnings - the severest possible, signifying a "danger to life" - have been issued for Lancashire in north-west England.
Weather experts forecast up to 5 inches of rain in the north of England - an amount approaching the average rainfall for the whole of December.