98 mustang gt

Need help, my son-inlaw has a mustang 4.6 w/ 4speed, he just changed all four tires and now has noticed a vibration in the rear of the car. He has had the tire rebalanced and the tire shop has replaced the two rear tires, but the vibration is still there. Do you have any suggestions what could be the problem? I think it might need new shocks in the rear, also, being a chevy guy and not knowing fords, I noticed when looking at the rear end, that the car has four shocks 2 up and down and 2 forward to rear mounting on the axle house to the frame could those have gone bad and cause the vibration. again these parts are probably all original stuff. Any help would be great.
Thanks Tony C.

So did he get the tires swapped onto the same rims that were originally on there? If so, it still sounds like a balancing issue, or possible cheap tires that are out of round of have a heavy spot. I would bring it back to the place that mounted and balanced, have them recheck it and supply you with a print out of the specs.

Also the four shocks you are talking about, 2 are the normal rear shocks and the 2 horizontal shocks are called quad shocks. They were designed to prevent wheel hop and axle twist with the factory rear control arms and suspension. Usually people remove them if they replace the stock control arms with aftermarket boxed steel ones.