Emergency services were called at 2.06pm on Monday, January 13, to the crash involving two HGV lorries on the westbound carriageway.
One of the drivers, a man in his 30s, suffered serious injuries and was taken to hospital to receive treatment, according to police.
The other driver was not injured.
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The A303 was closed for several hours while the emergency services recovered the lorries involved before making the road safe for other road users.
The road was partially reopened at around 2am on Tuesday, January 14, as police thanked the commuters for their patience while the emergency services dealt with the incident and carried out enquiries.
As part of their investigation, officers are now looking to hear from anyone who was in the area or witnessed the crash, or the moments leading up to it or the aftermath.
Anyone who saw what happened or has any information, including dashcam footage that may assist the enquiries, is asked to call 101 quoting the reference 44250017318.
Alternatively, you can submit information online by going to hampshire.police.uk/contact/af/contact-us-forms/provide-more-information-about-a-road-traffic-incident/