An RAF helicopter and inshore lifeboat took the trainees off the 110- ton Royalist after it became stranded on a falling tide.
The ship's master, a pilot and 12 crew were staying on board and planned to try to refloat the vessel on last night's high tide.
A tug and rescue services were remaining on stand-by until the 100-ft brigantine was out of danger. The weather was described as good.
A rescue was launched when the Royalist got into trouble in the estuary, three miles north of the Severn Bridge and near Oldbury power station.
Reports said the vessel was listing more than 30 degrees as it was left aground.
A Sea King helicopter from RAF Chivenor, north Devon, and lifeboats from Sharpness and Chepstow were later brought in to take off the crew, who were landed ashore at Beachley Slip, on the Welsh side of the estuary and Sheperdine, Avon. No injuries were reported.
Mike Osborne, the district controller of the Swansea Coastguard, which was co-ordinating the rescue, said it was not clear why the Royalist had gone aground.
"Our prime aim is to ensure the safety of all of those on board and for this reason we began moving the crew," Mr Osborne said.
The Royalist, which was registered at HMS Dolphin in Gosport, Hants, was built in 1971 and travels mainly around Britain as a training vessel for sea-cadets. The brig had just left Gloucester docks after a visit to the local Sea Cadet Corps at the weekend. The 100-ft ship was built for the sea cadets and is crewed by their instructors. It was open to the public in Gloucester docks, Britain's most inland port, on Saturday, when cadets in full dress uniform took visitors on guided tours of the vessel.Reuse content