The 52 year old from Rugeley, who was a passenger, died at the scene of the accident on the B5062 at Tibberton on Sunday.
The driver, a 56-year-old man, was taken to hospital and has since been discharged.
The car, which police said was heading from Harper Adams University to Shrewsbury, mounted a grass verge and ended up in a field.
Police closed the road while the vehicle, which had rolled onto its roof, was cleared and the highway made safe again.
Four fire engines were mobilised from Hodnet, Newport and Wellington, while an air ambulance was also sent to the scene.
Officers investigating the accident are hoping to speak with people who used the road on Sunday, and have asked anyone with information to contact them on 101, quoting reference number 368s of August 5.
Alternatively, details can also be left anonymously by contacting the Crimestoppers free phone line on 0800 555111.