Across Britain, the number of homeless children has increased by 59% in five years, the charity’s report said.
In Scarborough, at the end of March this year, 38 children were reported as homeless.
It means one in every 516 children in the area was homeless, the second-highest rate in Yorkshire and Humberside.
Shelter says that trends from recent years show that levels of homelessness at Christmas are generally at least as high as in March.
The majority of homeless children are living in temporary accommodation, meaning they can be moved on at short notice.
In more severe cases, they could be living short-term with friends or family, or in hostels or bed and breakfasts – accommodation the report describes as “totally inappropriate” for children.
While legislation means children should never have to sleep rough, there are some extreme cases in which this can happen for a short time.
Across Yorkshire and Humberside, 822 children were recorded as homeless, at a rate of one in every 1,409 children.
Of them, 37 are in hostels or B&Bs, often with one family in a single room, sharing bathrooms and kitchens with other residents.
The regional rate is significantly lower than the rate across Britain, where it is one in 103. It means more than 131,000 children are expected to be homeless this year – nearly 50,000 more than five years ago.
Greg Beales, director at Shelter, said, “No child should be homeless. But for the generation growing up in the housing crisis, this is the grim reality for many.
“The number of children hidden away in hostels and B&Bs is enough to make anyone’s heart sink.
“These are not places for children. We hear about cold, damp – even rats. Young children are sharing beds with multiple family members, trying to play in dirty public corridors, and having to leave their block in the middle of the night to use the bathroom.
“Over the last five years, hundreds of thousands of children have known what it’s like to be homeless. The impact on these young people cannot be overstated. It doesn’t have to be this way.”
Minister for Housing and Homelessness, Heather Wheeler, said: “No family should be left without a roof over their heads, especially during the winter months, and we are working to ensure all children have a safe place to stay where they can thrive.
“Councils have a duty to provide temporary accommodation for families with nowhere to go, and we have been clear that they also have a duty to prevent homelessness in the first place.
“We are providing more than £1.2 billion to tackle all forms of homelessness, including amongst children, and introduced the Homelessness Reduction Act to ensure people at risk get help quicker.
“But we know we have more to do to tackle homelessness, and we will.”