Tens of thousands of residents have fled inland. No deaths have been reported, but the high winds are preventing emergency crews reaching many places.
More than 100,000 people are without power, and residents in the city of Corpus Christie have been told to boil their water.
Up to 5.8 million people are believed to be in the path of Hurricane Harvey, as well as the heart of America’s oil refining operations.
All seven Texas counties on the coast, from Corpus Christi to the western end of Galveston Island, ordered mandatory evacuations from low-lying areas. Four counties ordered full evacuations and warned there was no guarantee of rescue for people staying behind.
Reports of significant damage are emerging from Rockport, which was directly in Harvey’s path when it made landfall. The mayor urged residents who chose to stay to write their social security numbers on their arms to make it easier for rescuers to identify them.
Swells generated by Harvey are affecting the coasts of Texas, Louisiana and north-east Mexico.
Multiple tornado warnings have been issued and one has been reported at Sienna Plantation, just south of Houston. Tornadoes are possible throughout Saturday in middle and upper Texas and south-west Louisiana.
The key concerns are storm surges and flooding, with the storm expected to linger for days, potentially depositing 63cm (25in) or more of rain in some areas.
Even if the storm retreats to the Gulf of Mexico in a few days, meteorologists fear it could turn back to land for a second assault.
