Flat spot on the wheel.
Bad wheel bearing. (however its usually the front not the back)
Rotate the wheels and see if the problem travels with the a certain wheel
Maybe that thumping noise is the sound of another car smashing into the rear of your car.
worn torsen differential
Could be universal joint is finished. A bad flex disk
Check for a broken shock.
tire or wheel out of balance? broken mount on rear of transmission. I have seen where the threads for the bolts into the trans are ripped out.
You created a flat spot on the rear tires. Your car had a busted mount or bushing
Have that tire checked sometimes the belts inside can break and cause a thumping noise
check the rear drag links for wear the ball joints wear out a lot on them
problem could be the rear strut
More than likely the sway bar links - TSB on these
It may be your CV joints
It could be a suspension part such as a control arm. I just had replace the rear control arms on my 1993 Toyota Celica because the bearings in the control arms were worn out. It made a lot of rattling and thumping; when I replaced the arms the sound stopped.