West Point did not immediately identify the cadet who died, but said the incident is under investigation.
Officials said in a press release that 20 cadets and two soldiers were wounded when a Light Medium Tactical Vehicle was involved in an accident that occurred at approximately 6:45 a.m. off Route 293.
The injured have been transported to local hospitals, officials said in the release.
The Light Medium Tactical Vehicle, or LMTV, has a 2.5-ton capacity and a companion trailer.
Camp Natural Bridge is a cadet summer training site near West Point’s main campus.
West Point thanked local and state emergency responders for their assistance on the scene.
UPDATE: 7:30 p.m. from the Associated Press
WEST POINT, N.Y. — A vehicle loaded with West Point cadets on summer training overturned in rough, wooded terrain Thursday, killing one cadet and injuring several others, the U.S. Military Academy said.
The tactical vehicle operated by two soldiers overturned around 6:45 a.m. as it was headed to a land navigation site as part of standard summer cadet training, said West Point's superintendent, Lt. Gen. Darryl A. Williams.
The two soldiers were injured along with 19 cadets in the Class of 2020. Williams said none of the injuries were life-threatening. Injuries included broken arms and facial abrasions, an official with the hospital at West Point said.
Williams said none of the injuries were life-threatening. Injuries included broken arms and facial abrasions, an official with the hospital at West Point said.
"It is not common for these vehicles to turn over. It is very rough terrain," Williams told reporters at a briefing near the accident site Thursday afternoon. "You can see the hills we have here."
Helicopter footage from WNBC showed a truck flipped over in a wooded area.
The investigation is continuing, Williams said, and "we don't know the details of how the accident actually happened."
The "light medium tactical vehicle" that rolled over has a 5-ton payload and an extended bed, according to West Point. That vehicle class has a passenger capacity of 20, not counting those in the cab, according to an Army technical bulletin.
It was not clear whether all the cadets were aboard the vehicle, as opposed to nearby, academy spokesman Lt. Col. Christopher Ophardt said.
Officials were notifying relatives and did not release the identity of the cadet who died.
President Donald Trump tweeted Thursday afternoon: "So sorry to hear about the terrible accident involving our GREAT West Point Cadets. We mourn the loss of life and pray for the injured. God Bless them ALL!"
Classes ended at West Point last month, but the academy runs summer military training exercises for cadets in the heavily wooded hills outside the main gates. The rollover occurred on a fire break road as the vehicle was leaving Camp Natural Bridge, where trainees live during the summer, Ophardt said.
West Point is on the Hudson River about 50 miles north of New York City.
It was the second cadet death at West Point this year. Cadet Peter Zhu died in February after a skiing accident. His parents made headlines afterward for their successful legal effort to retrieve his frozen sperm.
This story has been corrected to show that 21 people were injured, not 22, and that all of the injured may not have been passengers in the vehicle. Additionally, the headline has been updated to delete the incorrect number of injured.