Google has been testing self-driving prototypes since 2009, mainly around its Silicon Valley headquarters in Mountain View, California.
Google is sending a second specially equipped Lexus RX450h prototype this week to Austin.
Last month, the company began testing tiny, bubble-shaped self-driving prototype vehicles of its own design on public roads around Mountain View.
Google and other automotive manufacturers and suppliers have said the technology to build self-driving cars should be ready by 2020.
Google executives have said the company does not want to build its own self-driving cars, but would prefer to find a development and production partner.
But most major multinational automakers are developing their own so-called automated vehicles that are designed to control major functions such as steering, brakes and throttle without human effort.
The Google self-driving cars have humans on board who can assume manual control of the vehicles if necessary.
A Google press release on Tuesday quoted the Texas Department of Transportation as saying "we welcome and support Google's autonomous vehicle test" in Austin.
Both Google and Apple Inc maintain offices in Austin, an emerging technology hub in the southwest United States.
© Thomson Reuters 2015