The storm, which has even stronger gusts, is expected to be the worst to hit Texas for 12 years. Up to a 40in (1m) of rain is expected to fall.
President Trump has signed a disaster proclamation for the state, which will free up federal aid for the worst-affected areas.
Texas Governor Greg Abbott has warned of record flooding in multiple regions.
The category four storm has already brought down trees in Corpus Christi and thousands of residents have boarded up their homes and fled.
The mayor of nearby Rockport Patrick Rios urged the few people in the town's population of about 10,000 people not already to have evacuated to do so immediately.
The city manager said that people were trapped in a housing centre for elderly people, where the roof had collapsed and rescue teams were unable to gain access, according to CBS.
There have been long queues of traffic heading out of the storm's path.
Governor Abbot said it was obvious that Texas was confronting "a very major disaster", while deploying more than 1,000 National Guardsmen were to help with the disaster relief operation.
High winds began lashing the coast at nightfall on Friday as coastal water levels rose at the same time.
Harvey is the first major storm of the Atlantic hurricane season and has severely hampered Gulf of Mexico oil production and air travel.
It is expected that more than 40 ins (1m) of rain will fall over the next few days, generating storm surges of up to 12ft (4m).
The National Hurricane Center said storm surges may bring life-threatening floods in and around Houston.
Forecasters say the storm's path is uncertain but it is expected over the next few hours to be near or just inland of the middle of the Texas coast.
The White House said Mr Trump is likely to visit Texas early next week.
In pictures: Texas braces for Hurricane Harvey
The storm is likely be the strongest storm to hit the US since October 2005, when Hurricane Wilma struck the coast of Florida.
Wilma left 87 people dead, and was part of a record-breaking hurricane season that included Katrina, which devastated New Orleans and killed nearly 2,000 people in August of that year.
.The last category four storm to hit the US was Charley in August 2004.