The drums supporting your vehicle's rear brakes are vital. The brake shoes are often looked at as a main issue of bad brakes, but the drums can be a big problem if they are not balanced. Drums that aren't even in their weight distribution will cause vibrations, especially when higher speeds are reached. This can severely damage the suspension, and you need to get these drums balanced immediately. The exact method of balancing them depends on a lot of factors, like the type of drums and how much work you can perform on them yourself.
Raise the vehicle's rear end and support it on jack stands. Remove the rear wheels.
Remove the brake calipers and discs if the vehicle has them on the rear wheels -- remove the caliper's mounting bolts with a wrench. Then, slide the disc off.
Pull the brake drums off of the wheel studs. Keep at least one drum near the wheel it was installed on at all times to ensure you know the positioning of each drum.
Inspect the inside of both drums, and check to see if one drum has a balance weight that the other does not. Many newer drums don't require weights, meaning this won't necessarily be an issue.
Attach a weight to a drum that does not have one -- you'll need to weld the exact same type of weight in the exact same location as the other drum. It may be much easier to move on to Step 6.
Replace both brake drums with a new set that comes in a pair. A full new set should be perfectly balanced. Slide these drums into position on the wheel studs.
Reconnect the brake disc and caliper (if needed), and then reconnect the wheels. Lower the car.