Putting young offenders behind bars also makes them more likely to commit further crimes and be unemployed later in life, the New Economics Foundation said.
The think tank is calling for drastic cuts in the use of youth custody and is urging budgets for youth custody to instead be given to councils and the money reinvested in rehabilitation programmes.
Last month there were 2,195 children aged 10 to 17 imprisoned in England and Wales. Each place costs 100,000 a year and an extra 40,000 in indirect costs to society once the inmate is released.
The research coincides with the release of a documentary, The Fear Factory, which criticises the so-called "arms race" on law and order issues between political parties. The makers claim competing politicians have created a criminal justice crisis in the UK.
"Prison costs the public purse about six times more than sending a child to Eton," the report's author, Aleksi Knuutila, said.
"What really makes our obsessive use of prisons even more of a tragedy is that those resources could have been used to tackle crime much more effectively.
"The resources we now waste on locking children up could be spent on measures that would really keep our streets safer.
"All the research shows that prison is failing to rehabilitate offenders and isn't steering them away from crime.
"At a time when public services are being cut everywhere, we need to ask whether our spending is really delivering on safety in our neighbourhoods."
Juliet Lyon, director of the Prison Reform Trust, said: "Currently many children who are not a threat to public safety are put behind bars.
"Community measures have been shown to reduce offending much more effectively than any length of prison sentence."
John Fassenfelt, deputy chairman of the Magistrates' Association, said: "Custody really is the last resort and only used when all other measures have been tried and exhausted.
"It is worthwhile noting that in December last year the number of young people in custody was the lowest since the establishment of the Youth Justice Board.
"This decline is the result of a number of initiatives, not least the increased provision of community based programmes and better communication between sentences and youth offending teams.
"If more programmes such as intensive fostering could be available then the custody rate would almost certainly drop further."
A Ministry of Justice spokeswoman said: "A key part of our approach to youth crime is to prevent young people turning to crime in the first place.
"We believe young people under 18 should only be held in custody as a last resort and for the protection of the public.
"Latest figures show there are 20 per cent fewer first time young offenders under 18 years of age than a year ago and the frequency of youth re-offending has fallen by nearly a quarter since 2000.
"In November we made the biggest change to the youth justice system in a decade when we introduced the Youth Rehabilitation Order, in order to simplify and ensure consistency of sentencing for young offenders.
"This gives judges and magistrates a number of options from which they can create a punishment designed specifically to deal with the offender before them.
"Last year we also committed 8.4m towards effective resettlement and rehabilitation services for young people leaving prison so they can turn their backs on crime. Now over 100 areas are receiving funding specifically for this purpose."