The police chase ended on the Moore Street roundabout, at the bottom of Ecclesall Road, after a grey Volkswagen Golf crashed at 2.30pm as officers were following the car.
A police chase was mounted after the driver of the Golf failed to stop for officers in the Twentywell Lane area of Bradway, at 2.05pm.
At least two police cars were damaged during the incident and two police officers suffered minor injuries.
Three occupants of the Golf – men aged 23, 22 and 27 – were arrested on suspicion of the theft of a motor vehicle.
The 23-year-old was also arrested on suspicion of dangerous driving and being over the prescribed limit.
All three remained in police custody last night.
Anyone with any information should call South Yorkshire Police on 101 and quote crime reference number 430 of September 11.
More to follow.