Removing tree roots?

I had a Chinese Elm tree removed and the stump grinded out over 2 years ago. The root system was pretty extensive. I have been waiting to plant lawn in the yard, but little sprouts/shrubs keep popping up all over my yard. I've tried everything from Roundup to digging the roots out. Nothing has stopped the weekly popping up of new little trees. Will I ever be able to plant anything in my yard again? How do I get rid of the roots from a tree that has been gone for over 2 years?