Experts predict that the River Ouse at the Viking Recorder will soar above its normal range (1.9m), peaking at 4.35m on Friday night (September 27).
The highest ever recorded level in this location is 5.4m, on November 4, 2000.
Environment Agency predictions are subject to change, depending on how much rain falls through the remainder of today.
A yellow warning for rain has been issued by the Met Office for today (Thursday, September 26) in York and North Yorkshire.
The Met Office warns that there is a "slight chance" of power cuts and loss of other services to homes and business while the warning is in place.
A spokesperson said that there is a "small chance" of flooding while the warning is in place, adding: "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."
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