Here’s the whole thing on YouTube.
The 55 is the real star of the film. 
Yes, one of my favorites also - I recommend the Criterion Collection Edition.
Just a little useless trivia…
The '55 is the SAME car from the American Graffitti movie that Harrison Ford (AKA: Bob Flafa) drove.
There were three black 55’s in American Graffiti, two of them were used in Two Lane Blacktop.
One had a 427 the other (the stunt car) had a 454.
Two of my favorite quotes in the movie. “not bad for a home grown” and “make it 300 yards and you got a race mother F#@$”.
That’s correct. I just didn’t get that detailed. Last I read, the same guy owns BOTH Milner’s Coupe and the 55. And from an equipment standpoint, the 55 would have blown the Coupe completely off the road via the tunnel-rammed dual quad big block vs. a Mani-Fre set-up on the 327 in the Coupe.
I Googled it.
As for the coupe:
Hey, nobody can beat him, man. He’s got the fastest…
Let’s not forget a couple of great low key performance by Dennis Wilson and James Taylor. You gonna remake that with Justin Beiber and Ed Sheeran? I don’t think so… 
I hope you aren’t just now discovering this movie Andy. I have it somewhere on vhs, probably packed away in the basement with the player.
Mike, I’m writing a film analysis of it and it’s all up in my neurons.
I’m writing about how the '55 is a symbol of the hopeful post war period, a paragon of American postwar ingenuity (styling, the sbc, etc.), and the actual car driven in the film is a symbol of how the hopefulness of American in the 50’s was worn down in the 60’s and was a tattered reworked gray memory by the time the early 70’s rolled around. The shine had worn off the chrome of the 50’s with the Vietnam war and everything else that happened.
The 55 is as much a part of the team and as much a character in the film as Taylor and Wilson. Certainly it’s dripping with tons of symbolism.
and stuff…
Yeah, but Milner has icewater in his veins. To beat him, you have to at least keep it between the ditches and shiny side up. Don’t matter if you have a Hemi under glass or a 351c set on kill, if you can’t keep it right side up.
“Those satisfactions are permanent.”
The dvd has a lot of extra stuff and is worth getting if you like this movie at all. There is an interview with James Taylor where he talks a little bit about the car and one launch he did accidently with the car in reverse.