45-year-old Tracy Houghton died at the scene alongside her two sons Ethan and Josh, aged 13 and 11, and the 11-year-old daughter of her partner.
It is believed they were all travelling in the same car. The collision involved four heavy goods vehicles and four cars.
Police were called to the incident yesterday (August 10) around 5:10pm on the northbound carriageway between the East Ilsley and West Ilsley junctions.
South Central Ambulance Service also attended the collision, one man was flown by air ambulance to the John Radcliffe Hospital.
He is still in hospital being treated for serious injuries.
A man and a teenage boy were also taken to hospital with minor injuries and have since been discharged.
Nine other people sustained minor injuries and were treated at the scene.
The northbound carriageway of the A34, between Chieveley at junction 13 of the M4 and between the West Ilsley junction was closed until approximately 6.30am this morning (August 11).
A 30-year-old man from Andover was arrested on suspicion of causing death by dangerous driving and has been bailed until October 5.
Chief Inspector Henry Parsons, head of the joint operations unit for roads policing, said: “Our thoughts are with anyone affected by this tragedy. Can I ask anyone who witnessed the collision, including anyone travelling on the southbound carriageway who saw anything they believe is significant, to contact police.”
Anyone who has any information should call Thames Valley Police on 101 quoting URN 1109 10/8.