Dublin City Council has activated its major emergency plan as a result of widespread flooding in the city.
Sustained rainfall led to major roads, houses and one of the city's main shopping centres going under water.
An off-duty Irish police officer is missing in County Wicklow, close to where a river broke its banks.
Public transport was severely disrupted and in one part of the city an inflatable boat has been used to rescue stranded motorists.
There were three-hour delays on some major routes out of the city, and the Dublin Dart train service has been suspended.
The heavy rain also hit travellers along the east coast of Ireland with the Belfast-to Dublin Enterprise service being cancelled.
Two rivers which run into Dublin, the Dodder and the Camac, have overflowed.
Authorities said further problems could be caused by an unusually high tide which was expected on Monday night.
The Irish weather service, Met Eireann, has issued a severe weather warning for large areas of Ulster and east Leinster.