After Houston, Harvey is now bearing down on eastern Texas and Louisiana.
Torrential rain is set to cause more misery, with a trail of destruction already costing tens of billions of dollars and a death toll of at least 20.
On Wednesday Harvey, which began as a hurricane and then became a tropical storm, went on to batter a stretch of coast from Port Arthur, Texas, to Lake Charles, Louisiana.
It has been described as the strongest hurricane to hit Texas in more than 50 years.
The crucial energy hub in Houston remains out of action.
A curfew has also been imposed in Houston amid reports of looting, armed robberies and people impersonating emergency workers.
Many of the 30,000 people forced to flee their homes in Houston are being cared for in emergency shelters.
Volunteers are helping the authorities cope with the huge numbers in need of assistance.
Dr. Essam Girgawy, who volunteered at a church shelter, said: “I’m a physician and this is what I do for a living and whenever there is a need I come.”
So far in Texas authorities say close to 49,000 homes have suffered flood damage, with more than 1,000 destroyed.
Emergency teams using helicopters and boats have rescued more than 4,000 people to safety.
Officials say 132 centimetres of rain has fallen in Texas, an all-time record.