Police have plucked more than 3,000 people from flooded neighbourhoods across the city, with the coastguard's boats and helicopters rescuing another 3,000.
It's not clear what caused the craft to roll.
The analyst said State Farm, Allstate and Farmers have the highest market share of the Texas homeowner's and commercial property insurance market.
The storm marks the first time Trump has been tested by a major natural disaster at the start of his administration.
The Coast Guard said about 50 percent of its operational helicopters across the country are now in Texas.
Two more Texas prisons near the rising Brazos River are being evacuated. Measurements for Texas on Tuesday morning showed levels in some areas around Houston to be 25ft above "flood" level. The foreboding images of the incoming storm bands from Harvey were lighting up weather radar screens early Tuesday, the 12th anniversary of the day Hurricane Katrina made landfall in Plaquemines Parish on August 29, 2005.
Already, some 50 inches (127 centimeters) of rain have fallen over Houston, sparking massive floods across the city of 2.3 million people, and its wider metropolitan area of six million.More news: Hurricane Harvey makes landfall in Texas as Category 4 storm
It has been almost a decade since a hurricane made landfall in Texas and over 50 years since a major hurricane made landfall in Texas.
Besides the additional National Guard troops from other states, there are about 1,000 active-duty military forces in position to provide assistance if called up by civilian authorities, he said.
Rain continued to batter south Texas and Louisiana to the east, with another 60 centimeters expected on top of the 90 centimeters that have already drenched parts of the region.
Just when it seemed the situation in the eastern parts of the U.S. state of Texas could not get any worse, more extreme rainfall is expected in the coming hours. "They took in a lot of people after Katrina, if you remember", Edwards said.
While Harvey may make some of them reconsider, there's no such thing as retroactive insurance. Some worry that will cause the flooding to get even worse.
At least a dozen have been injured as a result of the storm, which crashed into Texas as a Category 4 hurricane on Friday night before weakening.
Some fear that may be more than the nation's fourth-largest city could bear.