Texas Department of Public Safety troopers say five people, including 4 children were ejected from their vehicle when the driver swerved to avoid a rabbit near Terrell.
It happened near the intersection of Texas 205 and County Road 236 Friday afternoon.
The car went through a fence, rolled and came to rest in a field several yards from the road.
The 25-year-old driver and a 7-year-old passenger were taken to Parkland Hospital in Dallas with serious injuries.
A 4, 5 and 7-year-old were taken to Children's Medical Center in Dallas. No word on the extent of their injuries.
Troopers say no one in the car was wearing a seatbelt.
Chopper 5 showed the car came to rest on its side and was heavily damaged.