The Wesley Mission report says that as well as financial stress, more families are being forced onto the streets by domestic violence and relationship breakdowns.
Anglicare says renting a home is now all but impossible for anyone living on government benefits, with fewer than 1 per cent of rental properties in a nationwide survey cheap enough for them.
Fewer than 10 per cent are affordable for families of four supported by both parents earning the national minimum wage.
More than four million Australians live solely on aged, disability and war pensions, unemployment benefits, and parenting allowances. Their average income is less than half the national average.
More than 5 per cent of the population earns less than A$22,000 a year and is in severe housing stress.
And the number of households in moderate housing stress has soared from about 900,000 in 1995 to more than 1.4 million.
The Wesley Mission says the typical homeless person is now more likely to be young, female and more often than not someone with children.
"It is a sad fact that nationally, almost one-third of homeless people who receive support are homeless families - and that number is expected to grow in the coming years," mission chief executive Keith Garner said.
"We need to find more places where families with two, three or four children can actually find some settled place."
The mission's report shows that one in five homeless people seeking support is now under 12, a further 27 per cent are younger than 18, and 15 per cent are aged 19-24 years.
Families are the most likely group to be turned away from homeless services while two out of every three children who accompany a sole parent are turned away each day.
The mission says most cheap housing provides only one or two bedrooms, and many more three and four-bedroom homes are needed.
