Shakes while standing still, or only when it's actually moving?
Only when moving:
Driveshaft U-joints worn out? Rear axle supports loose or broken, allowing the axle to twist and force the driveshaft into an extreme angle?
Shakes while standing still:
Automatic? Maybe the shifter is adjusted wrong and fluid pressure is leaking into two or more circuits at the same time? Like, it's trying to engage Reverse and Park at the same time? Does it drive forward just fine in all gears? No noticeable forward/reverse creep in neutral on flat, level surface?
The engine is under load when the trans in in gear, even if the vehicle is not moving (you have your foot on the brake). The torque generated will usually tend to tilt the engine/trans in one direction or the other, and sometimes parts that are normally not touching anything, may come in contact. Especially if you have a broken trans or engine mount that allows more tilt than normal. Typically, the exhaust pipe may start hitting the body, or the rear axle/differential, or even the driveshaft. My Nova had an aftermarket muffler on it that was installed by a blind man, apparently. It would tap and rattle against the differential cover and drive me nuts, before I fixed it. There is a dangerous way to check for parts interference under the car: have someone you trust sit in the car, engine idling and trans in reverse, and his foot firmly on the brake pedal. Put blocks on both sides of the wheels that are most planted on the ground (you may need to jack the rear of the car up a bit). Crawl under the car while the shaking is going on, and look for the source of the sound. Use extreme caution!
Of course this is useless if the shaking is present only when moving, I wouldn't want you to crawl under a moving car
73 nova
