The River Swale and the River Dee have burst their banks, making some roads impassable.
The Environment Agency has issued a flood warning for Arkle Beck at Reeth and Low Fremington.
The agency said: "Due to intense downpours the flood warning is now in force for Arkle Beck at Reeth and Low Fremington. River levels are forecast to rise significantly overnight due to further intense downpours."
Mountain rescue teams, North Yorkshire Police and the fire service are helping stranded motorists on the Grinton Moor road, between Grinton and Leyburn.
Video taken by North Yorkshire Roads police officer TC Grey shows the River Swale powering through the village of Grinton, spilling over one of its bridges.
Video posted by Inspector Paul Cording, of North Yorkshire Police, shows the road eroding on the B6270 between Downhome and Grinton.
An area outside Wensleydale Evangelical Church in Leyburn is also underwater.
Meanwhile, further west, the River Dee has also burst its banks.
Video from Thomas Beresford shows the roads around Cowgill and Dent Head Viaduct underwater.
North Yorkshire Fire and Rescue Service said: We're getting lots of reports of flash flooding around Leyburn and Reeth.
"Please don't be tempted to drive through flooded roads if you don't know how deep the water is, turn around and find another route.
"Please also drive slowly through flooded roads near to buildings, as driving through at speed can cause waves of water to enter the buildings."
There were also reports of vehicles stuck in floodwater at Whipperdale Bank, Stainton and the B6270, Ellerton Abbey.
A landslip between Dent and Ribblehead has also caused delays on the Skipton to Carlisle line, with disruption expected until the end of the day.
North Yorkshire County Council said in a tweet: "There is a lot of surface water in places across the county and the following roads are currently closed A6108 Bellerby to Leyburn including Bellerby village, C34 Runs Bank to Scarth Nick Moor Road, Leyburn, A6108 Walburn Hall, B6270 Cogden Beck (nr Swale Farm – Swaledale)."