Motorists have been advised to take care and avoid some areas.
The Mill Road/R593 in Skibbereen is flooded and is likely to remain closed all day, according to Cork County Council.
Meanwhile, flood levels in Bandon are expected to peak this afternoon. The situation is being monitored by the council and crews are on standby.
AA Roadwatch has said the Skibbereen/Caheragh Road (R594) is impassable near Derreeny Bridge (at the Drimoleague turn-off) due to flooding.
Park Road in Mallow is also impassable and a section of the N72 Fermoy/Tallow Road is flooded near the school in Kilmagner. AA says the road is passable, but care is advised.
Cork County Council said a number of areas are being monitored including the bridge in Fermoy, which “if necessary, will be closed in the early evening”.
The local authority’s emergency team can be contacted on 021 4800048 and flooding updates are available here.