The first one was at about 9.45pm on Tuesday on the A4117 near Cleobury Mortimer, where crews from the fire service, police and ambulance were sent.
A spokesperson for West Midlands Ambulance Service said they were called to Broome Green in the town at 9.53pm and found two people who had sustained "potentially serious injuries."
The spokesperson said: "Two ambulances, two paramedic officers and a Community First Responder attended.
"Upon arrival we found a man and a woman who were the driver and passenger in the car.
"They were both assessed and had sustained potentially serious injuries. They received treatment at the scene. Both were conveyed to Worcester Royal Hospital.”
A spokesperson for West Mercia Police said: "At around 9.45pm yesterday officers received a report of a collision on the A4117 near Cleobury Mortimer.
The fire crew found that one car that had come to rest on its roof but that no persons were trapped.
Shropshire Fire & Rescue Service's incident stop message was received at 10.16pm.
The second crash was at Hadley Road, in Oakengates, Telford, at 2.54am on Wednesday.
One fire crew was scrambled to the scene from Wellington Fire Station and they found a crash where one car had overturned on the highway.
No people were found to be trapped and no action was required by the fire crew.
A spokesman for West Mercia Police said their officers received a report at around 2.45am today that a car had overturned.
"Officers attended, no injuries were reported and the car was recovered," said the spokesman.
The fire service's involvement was declared stopped at 3.09am.