Well if this is the kind like I had when I was a kid, then not too far down. I actually just took down a set at my parents house that my mom was using for babysitting. I was surprised that the cement was only maybe 6-12" in the ground. It wasnt deep at all, but there was never a problem with it moving or heaving. I didnt even have to dig it out. I cut the swing set up and just pushed the legs out of the ground.