The Environment Agency expects the Ouse to be above the top of its normal range (1.9m) by 5pm at the Viking Recorder.
Tomorrow afternoon the river will peak at 2.92m, the agency said.
No flood warnings are in place for York.
A flood alert has been issued for the Lower River Derwent.
Areas most at risk include local roads and low-lying land around Stamford Bridge, Pocklington, Wressle, Wilberfoss and Elvington, an Environment Agency spokesperson said.
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