The system wouldn't have cars that flew exactly - instead, they would be suspended from thin wires you could barely see. According to English Russia:

It was called the "super string transportation system" and was claimed to come to replace the existing rail road technologies. The steel cords under great tension had to be stretched on the polls across all the country to support the high speed (up to 500 km/h - 300 mph) trains movement.

It would be sort of like a gondola system, only it would look more space-age. In fact, these images look like public transportation on another planet.

Plans for the trains were approved in the 1970s, and work began on them right away. As you can see from these images, the system was never very extensive but it was durable. This is what the tracks look like today.

This was a prototype of the cars they imagined using the tracks. Basically, it looks like a truck. It's also not suspended from a wire, but apparently that was part of a later plan.

This is an example of a contemporary super string car, put on exhibit recently in Moscow. It looks a lot more futuristic than those trucks, but it's still a long way from being a flying car. No word on whether the super string system outside Moscow will ever be revived.

via English Russia

Kidney writes:

My current home is near the top of Mt Washington, and several times a week I jog down this same street to catch the Metro Rail at the bottom of the hill. As I hike back up, panting, I sometimes imagine I'm being passed by one of the iron cars of the Los Angeles and Mount Washington Railway. Inside, the passengers in their colorless hats and collars sit on wooden benches gazing out at the passing front yards. And as they go by, I realize not one of them can see me.

So cool. Reminds me of the post we did a while back on the alternate history of public transportation projects that almost happened.

Ghosts of Mnt. Washington [via Dinosaurs and Robots]

According to Architectural Record:

Its gently curving span is suspended by 66 cables from a tilted 387-foot mast, anchored in concrete, that resembles a bolt of lightning. The mast is set at an angle to the deck of the bridge and it bends roughly halfway up, so the entire mast forms an angle of roughly 150 degrees. Cables are attached at various heights on its tapered top half, creating cross-hatched visual patterns as they seem to swirl out from the mast. At the sharpest bend of the bridge, the slightly concave, boat-shaped deck and the shape of the bend transfer the load to the ends of the bridge, which is 525 feet long; access ramps, clad in stone, add another 656 feet. A walkway on its southern side has glass decking and a glass railing.