The collision happened at 2.15pm on Sunday on the A488 between Minsterley and Pontesbury, involving a Suzuki Swift and Blue Kia.
Considerable damage was caused to both vehicles, with the Suzuki leaving the carriageway and coming to rest on its roof.
The driver of the Suzuki, a man aged 34 and the driver of the Kia a man aged 42, suffered serious injuries and received hospital treatment. Their injuries are not believed to be life threatening.
A passenger in the Kia, a 30-year-old woman, suffered minor injuries.
Enquiries are on-going an police are appealing for witnesses, in particular anyone who saw the Suzuki being driven before the collision.
Anyone with information should contact West Mercia Police on 101 quoting reference 388s 100319.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org