Up to 1972, Corvettes had chromed steel bumpers on the front and the back. Through the years these bumpers had taken various shapes - early on the exhaust pipes came through holes in the bumpers, and in some years these had been little more than decorative trim. But as the 1970s progressed, the U.S. Department of Transportation was requiring more substantial bumpers as a crash safety measure.
1974 was the big year for all automakers to upgrade their bumpers, which is why so many 1974 and 1975 model year cars have such big bulky ugly bumpers. Every automaker from Alfa-Romeo to Volvo had to ditch the old lightweight stainless steel or chrome bumpers and strap on these enormous steel-plate monstrosities, and the general practice was to sheath the new battering rams in plastic or rubber to try to hide what they were.
The Corvette fared better than most cars in this regard. Chevy started the transition for the 1973 model year with a rubber front bumper while retaining the chrome bumper in the rear. This is one reason why the 1970-1972 cars are more sought-after than the transition year 1973-1974 cars. For 1974, the new rear bumper was covered in a soft pliable plastic that came in two pieces, with a big obvious seam running vertically up and down the middle of the Corvette's back end. You can imagine the snarky comments that generated. But in 1975, Chevy went to a one-piece soft plastic rear bumper cover that worked pretty well, and they kept it mostly unchanged through the end of the C3 line in 1982.
It's pretty rare to have to remove the rear bumper skin, but there are a couple instances where you have to take it off. One is to repair cracked fiberglass in the rear fender arches, and the other is to get at the flexible fuel lines that run between the fuel tank and the hard fuel lines that run along the Corvette's chassis.
Before you take the bumper skin off, you need to undo the taillights - these are held in with two philips-head screws per light. Remove these and you will have access to the supporting rings, which also clamp the bumper skin to the bumper. These are held on with 7/16-head bolts. You will also have to remove a plate behind the license plate that clamps the bumper to the car. You will also find it much easier to do this work if the whole spare tire assembly (with its clamshell) is also removed.
The rear bumper is held onto the car by means of a series of 18 3/8-inch nuts that screw onto threaded studs (see photos) that are mounted on strips of sheet metal. The sheet metal strips are curved so that they fit around the top and sides of the bumper skin. Each strip is unique and fits in only one position - but that's easy to figure out. There are matching holes in the bumper skin and the fiberglass bodywork for the studs.
Taking the old studs out is harder than remounting the skin, because they're likely to be rusted. Your new strips will be shiny and smooth - and they come with new nuts and washers! You just have to be patient and work with a 1/4-inch rachet and a deep 3/8-inch socket, or with a 3/8-inch wrench. Many of the studs may simply twist off, which is actually easier than removing the nuts properly.
TIP: If you have been thinking about replacing the CORVETTE badge on the rear bumper, do it now because you need to have the bumper off to do that job.
Installing the new mounting strips is almost a reverse of the removal - except that the bumper skin is very flexible and there's some wiggle room in the mounting holes. So as you work from underneath the car, be sure to put the nuts on very loosely at first, and have a friend help you align the seams between the bumper skin and the fiberglass body. If you don't do this, it will take hours to get the bumper to line up properly. Then reinstall the taillight support rings, license plate support, and taillights when the perimeter is tightened down.
The best news is that if you refreshed your fuel lines while you were in there, you shouldn't have to do this job again for at least 20 years.