Ursula: maybe this will help
are you referring to elm trees? tall ones? if so, by cutting down either by yourself or with a tree/landscape service.
Popping up in your yard? Dig them up.
Spray foliage of short buckthorn or seedlings with a herbicide. Glyphosate (one brand name is Roundup) will kill all actively growing vegetation on which it is sprayed. Triclopyr will kill broadleaf plants and will not harm grasses when applied properly.
This weed killer recipe will work on elms and you can mix it yourself