Instead, the Phoenix free school in Manchester would offer students ambitious academic goals, outdoor activities and a demonstration of "martial values".
In the modern army, it says, these values are "self-discipline, respect and an ability to listen". There will be high standards of behaviour - but no demands to "get down and give me 50". The new 11-18 secondary school, which has yet to find a location, is being proposed by the Centre for Policy Studies, a thinktank, and is backed by Lord Guthrie, a former chief of the defence staff.
Its intended headteacher is an army captain, Affan Burki, and it may be housed on surplus army land, such as a "disused TA [territorial army] drill hall".
Tom Burkard, a research fellow at the thinktank who is on the steering committee for the planned school, said: "I want to get away from the idea that it is going to be a glasshouse or sin-bin.
"I want to ensure that kids are there because they want to be there. You need a stick somewhere - but if you have to use it very often, you've lost the battle."
Burkard makes the case for the school in a report co-authored with Captain Burki.
It says: "All the old remedies for poverty, under-achievement and alienation have been tested to destruction. The consequences were starkly before us on the streets of Tottenham and Croydon. But before we put troops on the streets we should consider putting them in our schools."
The proposal comes as the Ministry of Defence gives details of its redundancy programme and coincides with plans by the government to encourage former members of the armed forces to take up teaching, by providing sponsorship and a fast-tracked undergraduate route.
In a speech on Thursday, the education secretary, Michael Gove, said he wanted children have more male role models. A quarter of primary schools in England, around 4,000, have no male teachers.
Gove also announced that ministers are to scrap a requirement for teachers to record instances when they use physical force, as part of a wider move to "restore adult authority" in the wake of the riots.
In a speech delivered at Durand academy in Stockwell, south London, Gove said the regulations on the use of force inhibited teachers' judgment: "If any parent now hears a school say, 'sorry, we can't physically touch the students', then that school is wrong. Plain wrong. The rules of the game have changed."
Gove made a moral distinction between a "hard-working majority" and a "vicious, lawless, immoral minority". But he went on to examine what he said were the policy failures behind the "educational underclass". He said: "To investigate where the looters came from is not to make excuses because of background. It is to shine a light on failures that originated in poor policy, skewed priorities, and the deliberate undermining of legitimate authority."
Gove said there had been a slow erosion of adult authority, subverted by a culture in which young people felt able to ignore civilised boundaries. "The only way to reverse this dissolution of legitimate authority is step-by-step to move the ratchet back in favour of teachers."
Brian Lightman, general secretary of the Association of School and College Leaders, welcomed Gove's statement on the use of force against pupils.
He said: "The use of physical restraint is thankfully required very rarely. On occasions where it is needed, detailed guidance exists and staff fully understand the need to follow it to the letter."
The team behind the Phoenix free school is seeking a partnership with an existing academy sponsor. They have not yet submitted a proposal but hope to open in September 2013, unless their application can be accelerated. If successful, the school would be the first in a chain.
Burkard said the reason all its staff would be ex-military was "to ensure that the staff room is working from a common ethos as opposed to having people working at odds with each other".
But the school will not feature cadet-style military training. Burkard said: "I don't want people to think of it as an outpost of the army, but a community institution that happens to employ soldiers."
Guthrie expressed support for the proposal. "This would be no sticking plaster for the social problems our country faces. Rather, it would help to address deep-seated problems which are now increasingly apparent. If this school is a success, then it should serve as a model for a chain of hundreds of schools.
"We must hope that coalition ministers do all they can to expedite this extraordinary and significant initiative."
A spokesman for the Department for Education said: "We welcome the interest of organisations that have the potential to run great free schools."
The first free schools opened their doors to pupils yesterday. Aldborough free school, a primary in Redbridge in east London, and Krishna-Avanti primary in Leicester are among 24 new schools opening this week and next.