The red Volvo V50 they were travelling in failed to negotiate a bend on Rivelin Valley Road, Rivelin, and hit a tree at 5am yesterday.
Police said a 20-year-old driving the car suffered serious injuries while a 21-year-old passenger suffered serious and potentially life-changing injuries. Both remain in Sheffield's Northern General Hospital today.
Firefighters yesterday described how the two men had become trapped in the damaged vehicle and they had to use specialist equipment to cut the roof off to free them.
Steve Jones, watch manager at Rivelin Fire Station, said: "The damage was very serious to the extent that the engine was no longer part of the vehicle.
"The two occupants sustained major injuries and we worked as quickly as we could to get them out of the car and off to hospital."
Crews from Sheffield Central and Tankersley stations provided additional support and emergency services were on the scene for a couple of hours.
Police are now appealing for witnesses to the collision.
Anyone with information is asked to ring officers on 101 quoting incident number 192 of 15 July 2017.