According to the Wikipedia entry for this film:
"The hero's white car, named the "Leslie Special" was specially built by Warner Brothers to resemble a Thomas Flyer, the car that won the 1908 New York to Paris Race. According to the Petersen Automotive Museum, four "Leslie Specials" were built. One of the four appears painted green in the 1970 Warner Brothers film The Ballad of Cable Hogue—the grille can be seen bearing the words "Leslie Special". Another of the four is at the Tupelo Automobile Museum listed as a 1963 Leslie Special Convertible.
The villain's black car was named the "Hannibal Twin-8"; five were constructed. One of them is on display at the Petersen Automobile Museum, powered by a Volkswagen industrial engine. Another is at the Volo Auto Museum in Volo, Illinois. This model includes a prop "cannon" and a working smoke generator. The Volo museum describes the Hannibal Twin-8 as built by Warner Brothers at a cost of $150,000, powered by a Corvair six-cylinder engine with three-speed manual transmission and six wheels. All four rear wheels are powered by a chain drive."