Homes have been evacuated in Snaith after the River Aire flooded.
People forced to leave their properties have been encouraged to attend the local church for shelter and refreshments.
Drivers have been advised to avoid the area with the A1041 north of Snaith closed in both directions and cars submerged in water.
Firefighters have been putting sandbags outside houses as well as saving animals from the flood water.
Locals described being shocked by the speed at which parts of the town flooded with water rising within an hour.
One person told the BBC he could only access his house by going over the railway lines at the back of his property.
The council said that 10 properties - seven commercial and three residential - had flooded.
Mathew Buckley, head of legal and democratic services, said it was a "challenging situation" with "further overtopping" of the River Aire anticipated during high tide at 22:00 GMT.
Properties have been evacuated on Buttle Lane while there is also disruption in the nearby village of Gowdall.
Speaking from Snaith, BBC reporter Phillip Norton said businesses had been affected, with a car dealership and vintage motors shop submerged in the water.
He said: "There is what can only be described as a torrent flowing across the road near the railway station here, when we arrived you could hear a roar in the air and it was the sound of water gushing over the top of the river bank."
Snaith Primary School closed early while the Snaith School stayed open but parents affected, or whose journey home would be disrupted, were encouraged to collect their children.
The primary school will remain shut on Wednesday while the Snaith School said it would keep parents updated on its plans.
The properties which have flooded are on washland, according to the Environment Agency (EA).
The EA said the washland is "designed" to store water and manage flood risk from the River Aire.
It warned that washland could fill to capacity over the coming days from the "very high volumes of water in the system".
The EA, which has mobilised more than 1,000 staff per day since the start of Storm Dennis, is urging people to check their flood risk and remain prepared to take action.
Caroline Douglass, director of incident management at the EA, said: "It is devastating to see your home or business flooded, and as the case is for some, be asked to evacuate.
"We urge people to stay up to date and listen to the advice of emergency services."
The lower River Aire has been causing concern since the weekend with a handful of homes reported to be flooded in nearby Hirst Courtney, on the opposite side to Snaith.
Fire crews from Tadcaster have been sent to the village to pump water out of the neighbouring fields.
The River Ouse in Cawood also remains of concern to the EA with extra sandbags put in place outside properties.
While in York, the Ouse is expected to remain remain high for the next few days with a predicted peak of 4.6m early on Wednesday morning.
The EA has forecast ongoing flooding for the coming days, with England having seen more than 200% of its average February rainfall, and some areas experiencing a month's worth of rain in 24 hours.