Met Éireann has issued three weather warnings around the country.
A yellow wind warning has been issued for Wexford.
The forecaster says north to northeast winds will strengthen this afternoon and evening with speeds of 60 to 65 km/h with gusts between 90 and 110 km/h expected in coastal regions.
Storm force winds are also likely offshore and also possible along cliffs.
Winds will peak later today but will remain very strong overnight into tomorrow.
While a warning for Dublin, Louth, Wicklow and Meath will see very strong north to northeast winds developing on Monday afternoon and continuing until Tuesday morning.
Winds will reach speeds of 55 to 65 km/h in coastal regions, with gusts between 90 and 110 km/h.
Storm force winds are also likely offshore.
And a status yellow rainfall warning is also in place for Wexford and Wicklow.
Met Éireann say heavy rain is expected, more especially in coastal areas with totals 25 to 45 mm and a risk of spot flooding.
Tonight will also see some falls of sleet and snow, mainly affecting high ground, as temperatures fall back to 0 to 3 degrees Celsius.
Tuesday is set to be cold and blustery, with rain and sleet in the southeast clearing during the morning.