Young children in particular are at high risk of breaking or fracturing a bone or receiving a joint dislocation, warns the American Academy of Paediatrics (AAP).
Most injuries result from children falling off the trampolines and from collisions when more than one child is bouncing, they say.
The academy also doubts that safety equipment such as protective mats to cover the springs, and guards to stop children falling off, work effectively.
Trampolines are now a common feature in many family gardens.Sales tripled in 2005, according to John Lewis, and have risen slowly ever since.
Dr Michele LaBotz, who co-authored a new AAP policy statement on their dangers, said: “Paediatricians need to actively discourage recreational trampoline use.
“Families need to know that many injuries occur on the mat itself, and current data do not appear to demonstrate that netting or padding significantly decrease the risk of injury.”
Three-quarters of injuries occur when more than one person is on a trampoline, according to studies she examined. Common injuries in all age groups include sprains, strains and contusions.
Children under five are at particular risk, with 48 per cent of injuries in this age group resulted in fractures or dislocations.
Falls resulted in about a third of injuries and the AAP warned that these “can potentially be catastrophic”.
Although the academy advised that adults should supervise trampolining at all times, it cautioned: “Many injuries have occurred even with adult supervision.”
It continued: “Failed attempts at somersaults and flips frequently cause cervical spine injuries, resulting in permanent and devastating consequences.”
Three years ago British doctors at Kingston Hospital in south-west London issued a similar warning, saying that a combination of “inadequate adult supervision, several people using the trampoline simultaneously and insufficient safety equipment seems inextricably linked with injury”.
But Professor Mark Batt, president of the Society for Sports and Exercise Medicine, said parents should also consider the health benefits of trampolines, rather than throwing them out.
He said: “As a doctor who is very concerned about physical activity levels in young people, I’d be very concerned about putting off a group of children from trampolining, who otherwise wouldn’t be very active.”
He noted that girls, who tend to be less active than boys, were often especially keen on trampolining.
Prof Batt also said some of the evidence on which the AAP had based its advice was weak, explaining that the studies did not show how many hours of trampolining, on average, led to an accident.
“The incidence might be very high, or it might be very low. We don’t know,” he said.He also thought it likely that safety nets and protective mats did actually reduce injury. However, he agreed with the advice to always supervise activities and not let on more than one child at a time.
A spokesman for the Royal Society for the Prevention of Accidents said: “Trampolines can be great for exercise and good fun if enjoyed safely by following a few simple guidelines.
"But a safety net is not a substitute for adult supervision.”