One recruit said of an instructor: "Yeah he beat me up... Kicked me around. Punched me."
Despite examples of good practice, two recruits claimed they were forced to the ground, one with a rifle loaded and ready to fire.
One corporal urinated on a recruit's boot, and more than one young soldier said he was punched in the face by his instructor.
Another recruit said his hand was so badly injured in a beating he could not salute properly.
In a statement the MoD said it had already been in the process of investigating several of the cases brought to them by the BBC documentary team.
"...where allegations were new, we immediately launched further investigations," it said.
"We are, however, unable to comment on the details of specific cases so that we do not prejudice ongoing legal processes."
Russell Sharp signed up and spent six months training
It said: "Bullying is absolutely unacceptable and fundamentally at odds with the Army's core values."
It added: "All soldiers are made aware that if they are a victim of bullying then they can complain either through their chain of command or to the independent Service Complaints Commissioner.
"We keep the standards of training across all Army facilities under constant review to ensure that the core values are being observed, and our training establishments are also the subject of continuous scrutiny by external, independent authorities."
The Catterick incidents were of a different nature to those highlighted by the investigations into Deepcut Barracks in Surrey between 1995 and 2002.
At Deepcut, four recruits - Geoff Gray, 17, from Durham; Sean Benton, 20, from Hastings; James Collinson, 17, from Perth; and Cheryl James, 18, from Llangollen, north Wales - died from bullet wounds in separate incidents.
Army investigations found they had taken their own lives, although an inquest recorded a suicide verdict for Mr Benton, and open verdicts were recorded for Miss James, Mr Gray and Mr Collinson.
Joke comes close to uncovering truth about reporter
Their families suspect the recruits may have been murdered, or driven to suicide by bullying, and they have repeatedly pressed for a public inquiry.
One of the investigations carried out after Deepcut looked at the way recruits are treated and trained.
It accepted the Army had made changes but warned that if new evidence revealed trainees' lives and welfare were still being put at risk the review would recommend a public inquiry.
An independent review into the circumstances surrounding the deaths of the four soldiers at Deepcut was headed by Nicholas Blake QC and published in 2006.
Mr Blake said there was no evidence the four were "bullied to death", but he found "clear evidence of foul abuse of trainees" at the barracks.
The review found some soldiers at Deepcut in the period the deaths took place had been beaten and sexually abused by their instructors.
However, Mr Blake rejected calls for a public inquiry, recommending an independent Armed Forces ombudsman be appointed to deal with complaints from soldiers.
The Army also introduced a new two-week training course aimed at all instructors.
The Undercover Soldier will be shown on BBC One (except Northern Ireland) on Thursday 18 September at 2100 BST.
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