Heavy rain and flooding forecast
Road users have been urged to take extra care as up to 40mm (1.6in) of rain is forecast in some parts of the country.
Flash flooding is expected in north and east Leinster, as well as most of Ulster, due to heavy rain.
Met Éireann has issued a weather warning to the general public, as well as a small craft warning to fishermen as winds reach force six or higher throughout the day.
Winds are also expected to reach gale force tonight on coasts from Erris Head to Malin Head to Wicklow Head.
It will remain dry in the south of the country, but heavy rain will continue overnight in the north-east.
Showers will continue tomorrow and on Wednesday, with strong and gusty northerly winds reaching gale force at the coasts.
Weather warnings have also been issued in the UK, which experienced strong wind and rain yesterday.
In London a woman was killed by a falling tree branch in Kew Gardens during rain and gusts of wind close to 30mph, police said.
The woman, believed to be about 30 years old, was pronounced dead at the scene yesterday afternoon, on a day when strong winds and rain lashed the country.
Wind speeds of up to 120km/h and rainfall of up to 60mm in some regions of the UK over the next 24 hours and the Environment Agency issued 56 flood alerts.