One woman, who asked not to be named, posted on Facebook: “About 12 minutes ago we witnessed a major accident as the A343 merged onto the A34.
“Four military vehicles were moving very close to each other and as the vehicles tried to rejoin the road, one of them overturned and rolled twice.
“Another convoy crossed the central reservation trying to avoid the collision, causing another collision on the other side of the road.”
The Ministry of Defence said it was aware of a collision involving two military vehicles, but added it could not comment further.
National Highways said the A34 had been closed between the A343 and the A4 due to “significant damage to barriers” at the scene.
Shortly before 10:30 p.m., a tweet announced that the road had been reopened.
Hampshire Police said in a statement: “A man in his 30s suffered a serious leg injury and was taken to hospital.
“A man in his twenties suffered a serious arm injury and was also taken to hospital.
“The police have carried out a number of investigations and would like to appeal to witnesses.”