Met Éireann has issued a status yellow rainfall warning for Leinster, Connacht, Cavan, Monaghan and Donegal.
The warning is in place until 6pm on Sunday.
It will be very wet in many areas with intense and thundery downpours predicted. Totals of 30 to 40 mm are likely, highest over Leinster, where values on some mountains may get up to 50mm.
The heavy rain will gradually become confined to Ulster during the evening, but some very heavy falls are likely in parts of east Ulster.
Motorists are asked to drive with care. There are very wet road conditions in Co Monaghan, particularly in the Ballybay area where there is flooding on some routes.
Monday will be cool and bright and will feature a mix of sunny spells and scattered heavy showers. Unsettled conditions will persist throughout the week ahead.