The heavy flooding caused a bridge in Grinton to collapse under the strain of the downpour after a month's rain fell in just four hours.
Many roads, including the main road between Grinton and Leyburn, were shut after more than 3.2inches of rain fell in the Yorkshire Dales.
The monthly average in the area for this time of year is 3.5inches.
North Yorkshire Fire and Rescue service said it was called out to more than 100 calls in the area.
The fire station is Leyburn was also flooded as crews battled to help people stranded in houses and cars stuck in water.
A spokesman for the service said: "North Yorkshire Fire and Rescue Service received approximately 115 calls to flooding incidents in Leyburn and Reeth on the evening of 30th July.
"We had several appliances, as well as our swift water rescue teams and high volume pumping appliance within the area attending various incidents involving flooded properties and cars stuck in flood water."
Richard Hay, rescue controller at Swaledale Mountain Rescue Team, said the evening was "one rolling incident".
He said: "We deployed our members and boats. It was pretty much a rolling incident and we attended around six separate incidents.
"People were trapped upstairs in flooded houses and we provided welfare checks on them, then our colleagues from the fire and rescue service evacuated them.
"Businesses in the area will be affected by a loss of visitors. It is the busiest time of the year for tourism and businesses that rely on visitors will lose out because the villages have been cut off."
Nigel Smith, head of highway operations for North Yorkshire County Council said: “Last night we had inspectors out from the beginning of the severe weather event checking flooding hotspots.
“Working with the emergency services and mountain rescue we took steps to check on vulnerable people and closed some roads due to flooding, as a precautionary measure in the interests of public safety.
“We also identified rest centres in case they were required and we are pleased to say they weren’t.
“With the other emergency responders, including Swaledale Mountain Rescue Team, we coordinated the rescue of seven people who were trapped on highways by the sudden flooding.
“This morning we have deployed all our available resources to check known areas of flooding, or road and bridge damage, and also to ensure that the remainder of the highway network is safe for the travelling public to use.
“We will have greater detail once all of the inspections are complete and we can then assess next steps.”
The environment agency said a flood warning remained in place this morning and some routes remain shut.
More rain is expected as the Met Office has issued a yellow warning for rain for much of the north of England.
The Met Office said: "Rain will be persistent and heavy in places across parts of central, northern and eastern England and northeast Wales at first on Wednesday.
"During the day rain may turn more showery in places but with a higher chance of thunderstorms by afternoon.
"Some parts of northern England could see as much as 40-60 mm of rain through Wednesday, while thunderstorms could produce as much as 30-40 mm in 1-2 hours."