Need to check the rear u-joint in the drive shaft.
check the fluid in the rear end it might be dry causing medal to grind causing a clunk noise or the gears in the rear end or worn done causing it to do the same thing
Pull the rear wheels off and check the brakes. Something may have broken or fell apart.
check engine mounts
If it's a clunk sound, check universal joint bearings and drive shaft bolts. Otherwise please describe noise.
sounds like some part of the rear brakes has come loose inside the brake drum pull brake drum off and check for what is broken
It shouldn't ...
You may have U-Joint problems
Could be a bad strut or shock No I have disconnected both rear shocks and knocking noise is still there whilst driving. Seems to be coming from rear. When stationary I can bounce rear of car up and down and hear noise with handbrake on but not with handbrake off. Any ideas?
U joint
Noise coming from engine in Oldsmobile Cutlass could be as a result of an oil leak in the rear of your engine. This makes the gears to wear off leading to severe knocking noise.
If the clunk, or thunk, is quite pronounced both when you are taking off and when you apply the brakes or before the vehicle comes to a full stop, the problem is most likely to be the U-joint(s) on the drive shaft is/are going bad.
Universal Joint needs replacing