Missouri Gov. Matt Blunt declared a state of emergency and mobilized National Guard troops to help. At least 19 Kansas counties declared local disaster emergencies.
River towns across much of Missouri were evacuating low-lying areas Tuesday or seeking help filling and stacking sandbags.
"We're scrambling around here," said Steve Mellis, who was volunteering near the central Missouri town of Easley as residents moved boats and equipment to higher ground.
Meteorologists now use powerful new flood prediction tools that combine rainfall data from Doppler radar and satellite with water levels from river gauges, reports CBS News correspondent Nancy Cordes.
One town meteorologists are most concerned about right now is Sibley, Mo., nestled in a bend of the Missouri river. The model predicts the river there will crest at 11 feet above flood stage on Wednesday and will remain above flood stage until at least Sunday, Cordes reports.
Two-thirds of the town of Mosby, 20 miles northeast of Kansas City, was already under two to four feet of water from the overflowing Fishing River, said D.C. Rogers, Clay County director of emergency services. He said the town's 242 residents began evacuating Monday morning. By evening, only one route into the community remained open.
Mosby's flooding could have been worse. Rogers said authorities managed to plug a damaged dam with sandbags. That private earthen dam holds back a 20-acre lake. If the dam broke, its water would flow into Clear Creek, which runs into the Fishing River and through Mosby.
"Last word I got is it's holding," Rogers said. "Hopefully, the waters will recede, and that guy can fix his dam."
"It hasn't gotten this much water since 1993," he said.
As residents of Parkville, Mo., braced for the storms, there remained a glimmer of hope: the water level is 10 feet lower than it was in 1993, reported Sophia Wharton of CBS affiliate KCTV.
Evacuations were voluntary in several western Missouri counties, but a mandatory evacuation was imposed in Parkville, just across the Missouri River from Kansas City, said Jessica Robinson, a spokeswoman for the governor.
Communities across the central Plains faced flooding from the weekend-long thunderstorms that spawned the deadly tornado that wiped out Greensburg, Kan.
Parts of Missouri, Iowa and Kansas received four to eight inches of rain in a 24-hour period, the National Weather Service said. In some areas, Tuesday morning was the first time in several days that rain wasn't falling, but runoff was still raising streams and rivers.
Flooding in Oklahoma was blamed for the drowning death of a man whose car was swept off a county road. A Kansas man died when his vehicle overturned in a water-filled ditch near Wichita, Butler County officials said.
Nearly 1,600 people were urged to evacuate the southwest Iowa town of Red Oak on Monday as the Nishnabotna River rose out of its banks.
Levees broke near Willow Creek in the western Iowa town of Missouri Valley, and some residents had to be evacuated by boat Monday, said Mayor Randy McHugh. "Appliances are just floating around," he said Monday.
Authorities rescued about 500 people Monday from flooding around Topeka, Kan., said Dave Bevans, a spokesman for Shawnee County emergency operations. Officials reported similar evacuations in Saline County, about 100 miles to the west, and flooding forced the evacuation of New Cambria, a town of about 150 people northeast of Salina.
Since the 1993 floods in the Mississippi and Missouri river basins, only two or three other flooding episodes have been comparable to what forecasters are predicting in the next several days, weather service meteorologist Andy Bailey said.
There will be differences though. The 1993 flood, one of the most costly and devastating in U.S. history, was caused by melting snow combined with heavy rain over a two-month period. After that, state buyouts of property on flood plains left fewer residences in danger of future floods.
"But make no mistake," Bailey added, "this is a major flood."
At the western Missouri town of Agency, the Platte River was forecast to reach 15 feet above flood stage Tuesday — less than a foot below its crest in 1993.
"At that stage, we expect the entire town of Agency to be flooded," Bailey said.
Elsewhere, flooding downpours from slow-moving thunderstorms will continue to swamp Western Texas, Oklahoma and even parts of New Mexico Tuesday and Wednesday, reports CBS News meteorologist George Cullen. At least another one to three inches of rain will fall, but many places could get four to six inches on top of the record rains that fell Monday.