Thumping and vibration problem

Okay guys this one has me totally stumped. I have a 96 Thunderbird LX sport. 69,000 Miles. I have 2 problems which seem to be from the same thing. First of all during hard acceleration or going over bumps there is a loud thumping from the rear end. Also, from 50 mph - 90mph there is a horrible vibration. It is best felt from 70-75mph. The vibration is very severe and seems to be from the rear of the car. But the vibration can be felt throughout the entire car. Floorboards, steering wheel, seats, dashboard, ect. I have had the tires balanced twice. Once by myself and once by belle tire. And I have also replaced the IRS bushings (they were worn out, but did not stop the problem). Please help!!

first of all, the thumping is most likely the upper shock bushings. i had the same problem on my 93 5.0 with only 70,000 miles. the upper shock bushing has 2 parts, the top of the lower one tends to get worn out allowing the shock to rattle in all directions. when you go over a bump the loose shocks thump like crazy.
you can check the bushing by jacking up the car by the frame until the shock is not in any tension/compression and try to rattle it around side to side, if it does, then that's what it is. you can also take the shock off the lower mount so it's just hanging by the upper and try rattling it. if this is the case, i would suggest new shocks, but just the bushing isn't that hard to find if you don't wanna drop the money. if the bushing isn't too worn, you may be able to space it with a washer on top of the upper busing but this is a band-aid.
this play in the shock could have some effect on the vibration of the car, as the suspension is allowed to travel for a short distance with no damping.

if that's not it, check for:
unbalanced driveshaft
bad wheel bearings
cheap tires (winstons are notorious for becoming unbalanced)
bad pinion/halfshaft bearings (will cause bad diff leaks too)
proper backlash on ring/pinion gear (find someone who knows what they're doing)

hope i helped

Check the driveshaft u-joints.

cv joints is something else to check

I have a 96 t-bird with the same problem and I have tried everything from putting a new rearend into the car.I still get that vibration around 65-75mph.If anyone has figured out what this problem is please email me, Thanks!

I had a loud thump, and there was a bushing missing from the stud holding the rear end. Replaced it, and haven't felt a vibration or thump from 0-125.