The crash occurred after the tire blew out on the van's front driver side, CBS Affiliate WWL reports. The van then hit the delivery truck traveling in the same direction on I-10, rolled about 200 feet across the median and landed on its tires in the oncoming lanes. No other vehicles were involved.
"It appears the tire blew out and the driver overcorrected," said Trooper Russell Graham.
Thirteen children riding without seatbelts were thrown from the van, including four of the dead who were found in the median of Interstate 10 near Baton Rouge, Louisiana State Police said.
All those killed and injured were aboard the GMC Safari minivan, and some were related, police spokesman Russell Graham said.
"I just saw the vehicle flip about three or four times and kids flying everywhere," witness Tammy Hall told WAFB. "It looked to be about 10 to 11 kids out of the car. And everyone started stopping, and we went to get her, and you could tell the driver was dead instantly."
The van didn't have enough seatbelts for the 13, and capacity likely wouldn't have exceeded 10, Graham said.
The driver, 38-year-old Mona Hines, was killed. She and a front-seat passenger, 28-year-old Stacey Hines, appeared to be the only ones wearing seatbelts
The 10 survivors were in critical condition Saturday afternoon at two Baton Rouge hospitals, Graham said.
State police said seven children remained in critical condition Sunday. Another two with moderate injuries are considered stable. Stacey Hines was also in stable condition.
Police identified the children killed as 2-year-old Ricky Hines Jr.; 12-year-old Lachante Floyd; 14-year-old Edward Barnes; and 14-year-old Ashley Hines.
The driver of the truck managed to steer to the side of the road and was not injured.
"The Louisiana Legislature just passed a law making it mandatory to wear seatbelts in both the front and back seats," Graham said. "This is a good illustration of why they did."
The interstate was closed in both directions for about three hours Saturday afternoon.
"Well it just points out, I guess, the fragile nature of life and death, particularly when you're going 70 miles an hour on the interstate, and one minor mistake can be so, you end up with tragic results, such as this one did," said Ascension Parish Sheriff Jeff Wiley.
CBS Affiliate WAFB in Baton Rouge reports the victims were from the Harvey area near New Orleans.