Ulmus parvifolia reseeds itself easily and I see it sprouting up adjacent to median plantings and in neighborhoods where there are older specimens.
I am not going to get into the contentious debate of what constitutes invasiveness, etc. I will let the smart people comment on that.
Dont plant it if you have a concern or are not convinced it would be prudent.

Rx

According to the Iowa DNR site, this is considered invasive by the following states: DC, NC, NE, NJ, VA, and WI. That doesn't necessarily mean that it's not invasive in other states. Georgia, for example, does not have an invasive list but there are many plants which are invasive here.

If you type the species name and the word "invasive" into a search engine, you might find more information.

Thank you both.
I will consider other trees.
The funny thing is, the Oklahoma forestry dept sells lacebark elm seedlings in quantity.
The blackjack oaks are dying, and the post oaks seem weakened and some have died. I suspect a fungus. Same thing with the trees on adjacent properties.
Maybe it's just the prairie trying to reclaim itself?
My neighbor thinks the trees were weakened from a fire 7 or 8 years ago, giving a foothold to insects and fungus.

I'm not quite sure why it is considered invasive in Wisconsin when there are no documented feral occurances in WI according to the USDA's plant's database.

Are you sure you are not referring to Ulmus pumila?? they share a common name, chinese elm.

But perhaps the USDA maps are not up to date.

The oaks may be dying due to Sudden Oak Death, which is an introduced fungus. Apparently this fungus hitched a ride into the US from China, on rhododendrons sold by Monrovia Nurseries.

Since you love elms, maybe try some American Elms. They have a high percentage of native Elm parentage, and are supposedly Dutch Elm Disease resistant. april

April, that is interesting about the fungus. You may be right.
The blackjack oaks are so tough, I've worn out a fresh chain on the chainsaw trying to cut one down. Once they get whatever it is that kills them, they just die, and you can push them over with one hand.
If you pull the bark away near the bottom of a dead one, the wood is black, as if it had been burned.

I bought (from the oklahoma forestry dept) some seedlings of redbud and american plum (natives) and Shumard oak (hoping that it will be resistant to whatever is killing the blackjacks) and the lacebark elm. I never thought about it being possibly invasive till later.

I'll try to get some seedlings of native elm from my Dad. He has one that has survived construction, and erosion of some of its roots by the creek, and still seems healthy 40 years after the house was built. Meanwhile I'll ask around about the lacebarks.

I don't know if this is helpful or not, but I was just trying to reseach what trees are along my street here in the bay area, CA and wandered upon this thread. I think they are the Ulmus parvifolia. Volunteers pop up all over the place, mostly along the edges of fences where I'm guessing the wind stops the seeds, and they grow incredibly fast. The ones along our street are huge and about 50 years old, and they are lovely. The volunteers might not be as crazy in other climates though, we just cut them back and it's not a huge deal. But now I do wonder about one we were going to let grow near our back fence...

.. Doing a search and found my old thread.. you live forever on the internet.

Ulmus parvifolia Chinese elm

Turned up on an Oklahoma Invasive list.
Interestingly, a colorado list recommends it over the Siberian elm (ulmus pumila). Although both species are on the oklahoma invasive list.

The trees I planted that were purchased from the Oklahoma Forestry service have been put to the test in the intervening two years. We had a very hot dry summer, then an early freeze, then a late spring hard freeze, then a very wet spring and mild summer. The deer were running amok. Here is the tally of 50 trees each. The ONLY trees that I can find surviving in native unimproved soil, outside the reach of the garden hose, are 5 stunted lacebark elms and a couple of redbuds. Two Shumard Oaks and four plums are stunted but alive in terrible soil, but they have been watered occasionally. The ones left to fend for themselves are dead. The lacebark elm in "good" soil is five feet tall.

I think that under the right conditions the lacebarks could easily be invasive. They will be replaced. The oklahoma forestry service does not list either of the elms on the order list for next spring. Glad to see they have taken them off.

I have lots of respect for the natives that can live in this soil.

We had Chinese elms when I was a kid. They got Dutch elm disease and died. My neighbors had a tree and every year I had to pull up thousands of Chinese elm seedlings, so I think growing them is rude if you have neighbor's in close proximity. I can't imagine how someone could favor them over our beautiful native elms, but to each their own I guess.