Cut grass down to soil with weed whacker don't hit roots! in order to kill the grass (don't use herbicides due to proximity of tree roots either) and smother with a biodegradable (i.e. not the ground up tire stuff)mulch.

This will keep the grass out, provide a unified texture under the treee stopping it from looking ratty, provide nutrients, and presever soil moisture. Mulch is the answer!

You could either do what the person above me suggested or if you would rather have something that you don't have to maintain quite as much you could plant some plugs of ground cover and just trim them back on occasion. These will do well in the shade of the trees.

Here is a link that might be useful: Furnache Lawn Care & Landscape

Ring each tree (remove sod by hand/shovel being careful not to damage roots and create a ring around the tree). Turn in some compost to the soil again being careful not to damage the roots and cover with 3' cedar mulch. Water thoroughly if in a dry climate. You have now added nutrients, given the trees a good drink, and preserved that moisture with mulch. The mulch will help keep the grass from returning. Weed out as necessary.

Dave

Here is a link that might be useful: Glacier View Landscape & Design, Inc.

Furnache, are you suggesting that the ground cover will crowd out the grass and therefore the grass won't continue to grow up through the ground cover??

Aside from what is good or not good over tree roots, there are a couple of competing issues--what kind of "look" is most important and what kind of maintenance. Questions include, does the idea of a bit of straggly grass just offend you 'cause it's not neat and tidy;, could it just look best somewhat natural; or does the area really look quite shabb;, are you interested in creating a specific garden area and tending it?

"Mulch" can give a uniform (though dull) appearance, but it then becomes a substrate for weed seeds; and also the grass will like to grow into it more than it did the bare ground--more so if you have an invasive grass species. It can be fairly easy to pull a few weeds out of mulch, but that depends. It depends on what's going on elsewhere on the property and in the neighborhood as to what seeds tend to crop up (?nearby maples? birds bringing specific seeds? ). Re: the grass, have to determine if need an impermeable, or nearly so, barrier between mulch and lawn. Then you have to think, mow-strip or weed-whack the edging.

similar but not exact for a ground cover--barrier issues, some weeding. These chores then contrasted with the upkeep of weed-whacking the lawn grass and how it looks on its best day. The more the area is VERY inhospitable to plant growth--say because of root competition and dryness--the more you might be able to have a lightly mulched area that doesn't grow much.

Also these issues are bigger or less big depending on the area you are dealing with--if a small area, you could try most anything and not lose too much. If a very large under-tree area, then more planning required.