new member w/tire size question

I'll attempt to post a photo someday when the weather is better. Just too cold to be fooling with the car at the moment. The last time and only the second time I had to car on the road the rear differential shook so badly at around 45mph I thought the driveshaft was coming out. I'm assuming the violent shaking was caused by tires since all 4 where flat when I first started working on the car.