She 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 could not comment further.
The National Motorway Authority said the A34 “would probably remain closed for several hours” between the A343 and the A4.
Hampshire Police said officers were called to the scene near Wash Water at 11.04am.
Police said: “Two men have suffered serious but non-life-threatening injuries following the collision on the A34 earlier today.
“A man in his twenties suffered a serious leg injury and was taken to hospital.
“Another man in his twenties suffered a serious arm injury and was taken to hospital.
“Both northbound and southbound lanes remain closed while emergency services deal with the incident.”