95 Caprice wanders during acceleration in the rear. HELP!

I recently purchased the car with 108K for only $500, its in Chicago so obviously it needs some attention to rust but runs great. The problem Im having is that when I press the gas pedal, the rear end sways to the side. I noticed today that the rear wheels point inward quite a bit.. enough to really notice. While the car is driving down the street, it feels perfect until i press the gas and when I let off.

need to put it up on jack stands and check the rear 4 link bars/bushing could be shot or one of the bars could be broken/bent

Definitely check your rear control arm bushings and the rear upper control arms. that sounds like a bad control arm or bushing, and these cars are known for not having the strongest upper control arms in the rear.

Thanks guys! I checked and the rear drivers side lower control arm bushings were completely worn. I was able easily move it by hand.

glad to hear you got it fixed