(CNN) -- Some of the worst flooding the mid-South has seen in decades is thought to be responsible for at least 11 deaths in Tennessee, the Nashville and state emergency management offices said Sunday.
Five of the deaths were in Davidson County, which encompasses Nashville, according to the Nashville mayor's Office of Emergency Management.
The rains have closed interstate highways, displaced thousands from their homes, prompted evacuations of hotels and nursing homes and turned city streets and parking lots into raging rivers.
Parts of the state have been drenched with up to 20 inches of rain, with more expected.
On Sunday night, multiple vehicles were trapped by water on Interstate 40 with water rising around them and with authorities working since the afternoon to get to the cars, according to the Office of Emergency Management.
Authorities have recovered bodies from a flooded house in Nashville and from an upside down vehicle floating on a flooded road, among other places, the mayor's office said in a release Sunday night.
Two young men who'd gone tubing on a flooded creek on Sunday evening were missing, the mayor's office said.
Also on Sunday night, authorities were working to evacuate more than 500 residents from the MetroCenter in north Nashville.
"All of our major creeks and the Cumberland River are near flood level, if not at flood level," Nashville Mayor Karl Dean said at a press conference Sunday, referring to the waterway that bisects Nashville. "The ground is entirely saturated, and the rain continues to fall. There's nowhere for the water to go."
The western two thirds of Tennessee has seen between 6 and 20 inches of rain since Saturday, with flooding spreading to Kentucky on Sunday.
In Nashville alone, more than 600 people were rescued from the water this weekend, Dean said.
Dean said Sunday that more rain has fallen in Nashville in the last 24 hours than has ever been recorded in the city.
"We are still at this point in rescue stage and will be until the water begins to subside," he said.
Dean urged residents to stay home Sunday and, if they could, to skip work on Monday, when Nashville schools will be closed and public transportation will be suspended.
Two of the three temporary shelters -- which can each house 200 people -- opened by the Nashville mayor's office had reached capacity by Sunday evening. The Red Cross reported approximately 400 people in 22 shelters throughout Tennessee.
The floods shut down parts of interstates 24, 40 and 65 around Nashville on Saturday and Sunday.
The floods left 36,000 houses around Nashville without power on Sunday, while all Davidson County residents were asked to use water for essential purposes only after flooding closed one of the city's water treatment plants.
Flooding also led to the evacuation of three area nursing homes, affecting more than 250 patients, Dean said.
Opryland Hotel expected to lose power Sunday night and staffers planned to ask their guests to evacuate, according to Janel Lacey, a spokeswoman for the Nashville mayor's office.
While some streams around Nashville were starting to recede on Sunday, the U.S. Army Corps of Engineers was planning to release dammed upstream water Sunday night, which could cause more flooding around Nashville, city emergency management chief Stephen Halford said.
The water needed to be released to keep the Army Corps equipment safe, Halford said.
The National Weather Service issued a civil emergency message Sunday to central and western Tennessee, telling people to stay off roads because too many are closed and people are getting stranded.
The weather service also issued a flood emergency Sunday for much of central Kentucky -- where tens of thousands were trying to get home after this weekend's Kentucky Derby -- and in south central Indiana.
In Louisville, Kentucky, the National Turnpike and Gene Snyder Freeway were closed on Sunday.
In addition to flooding fatalities, one Tennessean died over the weekend in a tornado in Hardeman County, the Tennessee Emergency Management Agency said Sunday.
The mayor's Office of Emergency Management in Nashville announced Sunday night that it had confirmed five fatalities in Davidson County -- which encompasses Nashville -- thought to be flood-related.