The yellow warning for Monday, September 30, encompasses large amounts of Ryedale and the coast.
It’s also in effect for Selby, but not York.
Rainfall is expected to begin at 8am on Monday, and last until 3am on Tuesday.
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In their warning, the Met Office said: “There is a slight chance of power cuts and loss of other services to some homes and businesses.
“There is a small chance that homes and businesses could be flooded, causing damage to some buildings.
“Where flooding occurs, there is a slight chance of delays or cancellations to train and bus services. Spray and flooding could lead to difficult driving conditions and some road closures.
“There is a small chance that some communities will become cut off by flooded roads.”
