One of our local nurseries will guide you toward shallow-rooted plants that they have in their inventory, or you can do a quick Google search for "plants that grow under trees" and get lots of ideas.
When choosing plants, however, consider the moisture of the soil under the tree(s) you wish to plant beneath. Soil under trees tends to be very dry because we don't really water mature trees and especially the soil around the perimeter of the tree.
A search for plants that grow in dry soil under trees is probably a more targeted way of discovering what will work in this very unique growing area. Some examples in this category of plants (shallow roots and alright in dry soil):
- lily of the valley
- coral bells
- lambs ears
For even more plant ideas for dry shady areas, click here.