The fire station in Leyburn flooded as crews were out answering emergencies.
The region is braced for more rainfall as the Met Office has issued a yellow warning for rain across much of the north of England.
Some roads remain shut and rail passengers faced disruption after a landslip between Carlisle and Skipton.
The fire service had to pump out some new homes in the town after the water hit, some of the residents had only moved in two months ago.
North Yorkshire Fire and Rescue Service said it received about 115 calls to flooding in Leyburn and Reeth on Tuesday evening.
A flood warning for Arkle Beck at Reeth and Low Fremington remains in place, according to the Environment Agency.
Some routes in the Yorkshire Dales remain shut but the fire service said there had been "no serious injuries".
Northern Rail said trains had been suspended between Ribblehead and Kirkby Stephen because of the landslip.
© The Great North Rail ProjectThe landslide near the Blea Moor near Dent means no trains are being allowed to pass.
The monthly average in the area for this time of year is 3.5in (89mm).
The fire service said: "If the road in front of you is flooded and you don't know the depth of the water don't risk driving through it."
© S/Sgt Wallace - SM Andy Creasey"Unbelievable scenes" in Leyburn, said Andy Creasey of North Yorkshire fire service
The event team said on Facebook: "Right now we are doing everything in our power to ensure our team on the ground is safe, and we can support all those who need help."
The event was due to be held between 2-4 August.
Farmer Raymond Caldert told BBC Breakfast the flooding in Grinton was the worst he had ever seen and, if the festival had been running, lives could have been lost.
He said: "I haven't seen anything like this.
"We had a storm here about 20 years ago, called Hurricane Charlie. I think this has been worse."
Mr Caldert added he had not lost any livestock but the flood washed away most of his 160 bales of silage.
Swaledale Mountain Rescue Team posted a picture of a collapsed bridge in Grinton on Facebook, urging motorists to "only travel if essential as many routes impassable" due to flooding.
© Swaledale Mountain Rescue TeamSwaledale Mountain Rescue Team posted a picture of a collapsed bridge
"The roads were a raging torrent and there were sheds and household oil tanks floating down them."
Mr Clough said his team spent more than eight hours searching properties in the area, rescuing about 10 people, but he added that North Yorkshire Fire and Rescue Service helped many more and estimated "100 or more" homes had been affected.
"Some homes had a metre of water in them - it was horrific," he said.
The Brymor Ice Cream parlour, near Masham, was caught in a freak hail storm that left some customers with minor injuries.
"Our parlour suffered damage to the roof, power failures and some visitors suffered minor injuries", it said on Facebook.
Leonie Garrard, who runs a clothing and interiors shop in Leyburn, said torrential rain caused water to come through the ceiling and left the town "cut off".
"I have never seen [anything like] this in my whole life. It has been horrendous."
Water flowed through the streets after heavy thunderstorms were followed by hail
"Silver Street was flash flooded and fire engines came to pump it out. The gardens are pretty devastated. It just looks absolutely drenched."
'Disruption and long detours'
Travel conditions across the northern part of the Yorkshire Dales have been described by police as "shocking".
The main road along Swaledale linking Richmond and villages including Reeth and Keld has been washed away near Grinton.
Another road from Grinton over to Leyburn now has a gaping hole where for years there's been a bridge over a stream.
A violent hail and rain storm further west caused a landslide to block the main Settle to Carlisle railway line between Kirkby Stephen and Garsdale.
With it being peak tourist season in the Yorkshire Dales, the damage will cause disruption and potentially long detours for both visitors and residents living over a wide area.
A farmer in the area, Andrew Loftus, said he had seen hailstones almost an inch (2.5cm) in diameter.
Gareth Walls, from Ripon, tweeted that they were "like pickled onions".
Comment: This comes on the heels of a heatwave followed by snow and hail in some parts, and, earlier in the year, unseasonably dry and warm conditions which led to wildfires across the UK: