Beeches are notorious for having an extremely dense mat of roots just below the soil surface. That, combined with the ability of the greater quantity of these roots to hog soil mositure and nutrients away from other plants, does make it very difficult to establish plantings underneath. That these are young trees may be to your advantage. The roots system may not be as well developed yet nor as widespreading.

I'd research some plants suited for dry shade, which is what this situation boils down to. A good many woodlanders will fit into this category. I'd send you my listing, but my climate is quite different and I can grow things you can't. Shallow rooted perennials and the minor bulbs are good choices - avoid larger, shrubby plants unless you find while cultivating in this area that the roots are not yet as big a deal as imagined. Hardy cyclamen and epimediums are the classic underplantings for beech woods in the UK. But bigroot hardy geranium, squill, eranthus, Anemone nemerosa and various groundcovers should work as well. Perhaps even hellebores, which are quite drought tolerant once estabished.

Thinning out some of the beeches should help, too.

We have a beech in our yard-it's beautiful, & right now, the old leaves are still hanging on, faintly shrimp-colored.

I haven't been very successful in getting much to grow underneath-part of the problem is the soil level seems much lower there, almost a depression, & I don't want to add topsoil, in fear of harming the roots. There are wild violets, some lamium, a unkillable humongous heuchera, & that's it...

I've been too busy working on other parts of the yard to worry about this spot-I am very thankful for the beech, it's a lovely, mature tree...

Thank you gardengal and thistle for your comments and suggestions.

I finally opted to cut some of my beeches and keep others where there roots might be much less of a problem. Will certainly go for dry shade perrenials and bulbs around them.

Excuse-me for my lateness to react. I did not received the email notice of your postings.