The National Weather Service estimated 12 to 18 inches of rain fell across the region, with totals reaching up to 20 inches in some areas, CNN reported.
The rain and flooding Monday prompted Lafayette, St. Landry and St. Martin parishes to declare states of emergency, The (Baton Rouge) Advocate said.
Lafayette Parish Sheriff's Office spokesman Kip Judice said Monday his department conducted at least "150 rescues throughout the day," including one involving 16 middle school students whose bus became stuck on a flooded road.
Among the hardest hit areas in Lafayette Parish was Carencro, where reports indicated water was as high as high as 8 feet on some roads, Sheriff's Office Capt. Craig Stansbury said.
Stansbury said fire department vehicles, tractors and watercraft were being used to reach people stranded in their homes and vehicles.
"A lot of things that we have at our disposal, we're just going to go ahead and utilize," he said. "Whatever it takes to get to the people."
In St. Landry Parish, Government Administrative Director Jessie Bellard estimated 2,000 people were affected by the floods.
People were using dump trucks to rescue residents trapped in their homes after major and secondary roadways experienced significant flooding.
"It's just a terrible situation," Bellard told CNN.
Maj. Ginny Higgins of the St. Martin Parish Sheriff's Office said flooding affected between 15 and 20 roads. Several people were rescued after being trapped in their vehicles, she said.
Many schools across the region were either closed or operating on a delayed basis Tuesday, The Advocate said. In some areas, schools were open but transportation was unavailable.
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