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.