As well as this, there will be a possibility of localised spot flooding, Met Eireann warned.
From 9 am Monday until 9 am Tuesday, the forecaster predicts heavy rainfall in Galway, Mayo, Sligo, Clare, Cork, Kerry, Tipperary and Waterford.
Winds are expected to be strongest along Atlantic coastal counties at first, but the strong winds will extend countrywide through the course of the Monday afternoon and evening, with the weather warning remaining in effect until 6am on Tuesday morning.
Heavy showers are expected in the eight counties under a status yellow rainfall warning.
"The rest of the country should have a mainly dry and bright day but with a good deal of cloud".
There is a Status Yellow Wind Warning in place for the entire country.
"There will be a bit of morning rain on Wednesday, but once that clears it will dry up and start to get much milder, apart from the west coast, which will stay wet", she said.
The early forecast for the weekend is also promising, Saturday is expected to be mostly dry and bright with some sunny spells.
After the stormy weather, Met Éireann is forecasting a big improvement.
Do not put away the brollies just yet, but Met Eireann is predicting warm temperatures of up to 18 degrees Celsius for this later this week. Highest temperatures of 11 to 13 degrees Celsius.
Thursday is also set to be warm with temperatures reaching up to 18C.
"It will be noticeably cooler on Friday with a few showers appearing especially in northern counties with highs of 12C to 16C", added Ms Lowe.