The warnings, made this morning, means people living near the river should take immediate action.
They have been put in force for the Esk at Lealholm, Egton Bridge and between Briggswath and Ruswarp.
An advisory note on the governent's flood information website said: "Following recent heavy rainfall the current river level at Lealholm is two metres and is continuing to rise and may lead to river levels affecting properties in this area.
"We will update this message as the situation changes."
An alert, meaning flooding is possible, has also been issued for the North Sea Coast at Bridlington.
Overtopping waves and wind-blown spray are expected in the South Pier area between 2.30pm and 5.30pm today.