When I put the car in drive the back end bounces and their is a rubbing noise

If the sound gets higher pitched with higher speed, you may have a bad wheel bearings. If the whining stays constant, there may be something rubbing like the brake backing plate (especially on drum brakes). Try putting your hand near the backing plate after you drive it a bit. The friction from rubbing will make it hot.

what you describe on the stands is normal differential action
rubbing /grinding noise can be bearings ,brake pads or calliper stuck on the slide pins

4wd?? Check CV shafts. Also look for whats rubbing. whre is the dirt rubbed off.

Did you check the fluid level in the rear end?

Hey Dennis,
Have you checked the lube level in the read differential? If its good, you have a wheel bearing going bad. To replace it, you will need to remove the axle.. This is not a hard fix, but you have to have the ALL the tools and you MUST put the rear end up on jack stands..DO NOT use a jack to hold the rear end up.. IF you are not very mechanically inclined, please take this to a qualified professional..
Auto Truck Repair Manuals by Chilton Haynes Clymer Factory
Jeep Cherokee 1984 2001 Repair Manuals
http://repair.chiltondiy.com/Pub/DIY/Product/1998-Jeep-Cherokee-repair-manual-online?ca=Repair&b=2229

You can drive on those struts untill it has no sping, and even then it is just dangerous because of bad handling. If it is you struts, then your car should bounce up and down if you tap the brakes, because the gas seal is leaking.
Struts are very easy to replace. The only special tool is a spring compressor, but it is easy to use, and you may be able to borrow one at an auto parts store like the AutoZone. Just a couple bolts at the top and bottom, and it comes right out. They cost less than $100.
If it doesn't bounce...it could be your half-shaft. Does it click when you make a turn backing up?

if the noise is while you are driving i would suggest rear wheel bearing, jack up both sides of the car at the rear and spin the wheels, the side where the noise is comming from will not spin as free as the good side. hope this has been helpfull

if possible have someone stand on the bumper and bounce. while you are under with a flashlight and try topinpoint the noise. if no noise while bouncing, the trouble is in the drive line not suspension. this noise could be something as simple as a seized shock bushing not or a u-joint. maybe the brake cable rubbing somewhere. good luck

Hi there. First thing to do is drive the car and when you start hearing the rattle, lightly touch the brakes. This effectively loads up the callipers and drive shafts. If the noise goes away, you might have rattling calliper pins (even new Honda’s suffer with this) or it might be either the inner or outer drive shaft couplings (more likely the outer drive shaft couplings) which may be cracked or badly worn. It could be 100 things but as a tip, get yourself a very good inspection lamp and check every nut and bolt connected to the suspension, brakes and engine support systems. You should be looking for signs of wear, rubbing and also rusting around and on joints – that’s a good indicator that things are not tight. Hope this helps. Scottech

If its a loud roaring sound when u drive check the hub assembly