Originally Posted by John P. Walsh
Try box squats to correct this. Work on you flexibility. Maybe you shouldn't be squatting right now.
I think that not squatting completely is bad advice. You can of course squat without problems, as long as you're doing it correctly. I know that you've already said that you aren't doing it correctly, but all you need is a strategy to combat this.
Your ass popping up could be due to a few reasons. If you're already hitting the depth and your back is still good, then it's not a flexibility problem. Could be one of many possible reasons, or a lot combined. Could be as simple as incorrect weight distribution of the feet etc. Some of the guys have already outlined some good things to try, and one of them may work for you, which solves your problem, but I used to do the same, and the cue that really helped me was to initiate the concentric part with your traps. Sounds crazy, but bear with me, when you initiate the movement with your legs it can sometimes cause the legs to extend and the chest to drop, causing your ass to pop up. Initiating it with your traps causes your chest to stay high and back angle (in relation to the floor) to remain relatively unchanged while your legs extend. Obviously if it were a front squat, then you wouldn't do this, but probably just drive the elbows up instead.
Make sense? May not work for you, but it did for me, so hopefully you'll benefit from my mistakes, and if it doesn't work for you, then maybe it'll help somebody you know.
Hope I helped