Up to 50 millimetres of rain is expected to fall in places.
A warning's going out to 15 counties over heavy rainfall over the coming days.
The Weather advisory from Met Eireann says 40 to 50 millimetres of rain is expected to fall in places until Tuesday.
It applies to Connacht, Longford, Offaly, Westmeath, Cavan, Donegal, Clare, Cork, Kerry, Limerick and Tipperary.
The periods of heavy rainfall may lead to some local flooding as river levels remain elevated.