People in five of the seven cars swept into the water about 10 miles south of Emporia late Saturday were accounted for Sunday morning.
Three of the children were strapped into the family's minivan, which was found 1½ miles from the scene. The fourth child was found Sunday morning about a quarter mile from the van. The father survived, but searchers were still looking for the mother, said Capt. Mark Conboy of the Kansas Turnpike Authority.
The National Weather Service said the Emporia area had received 8-12 inches of rain in 24 hours beginning early Saturday. More rain and thunderstorms were forecast Sunday for much of the Central Plains, and a flood watch was in effect for much of Kansas.
Near Emporia, where the cars were swept off the road, the rain flooded a creek running along the interstate. As the water continued rising late Saturday and spilling into the roadway, it forced cars to stop along the shoulder.
"It looked like a river going across the road," said the Rev. Steve Gordon, of the Bethany Missionary Baptist Church in Kansas City, Mo., who was returning to Kansas City when the water became too high.
"The concrete barriers (between lanes) were being tossed around like feathers," he said.
The storm that swept through the state Friday and Saturday dropped as much as 6 inches of rain on Topeka and Wichita. In Dodge City, in southwest Kansas, 4 to 7 inches of rain fell in a 24-hour period and several motorists had to be rescued from vehicles stranded in high water.
"We've seen some of the vehicles floating down the road," said Dodge City Police Sgt. Steven George.
The National Weather Service issued a flood watch effective until 6 p.m. Sunday for several counties in central and eastern Kansas. Heavy rain was expected to continue over areas that had already received 3 to 5 inches over the past several days.