Some suggestions for planting under trees:

perennials:

Adiantum pedatum maiden hair fern

 Arisaema
triphyllum Jack-in-the-pulpit

 Astilbe spp.
astilbe

Athyrium niponicum
‘Pictum’      Japanese painted fern

Brunnera macrophylla Siberian bugloss

Dicentra spp. bleeding heart

Dryopteris spp. shield fern

Epimedium xrubrum red barrenwort

Groundcovers:

Aegopodium podagraria snow on the mountain

Ajuga reptans bugleweed

Asarum canadense wild ginger

Convallaria majalis lily of the valley

Galium odoratum sweet woodruff

 Lamium spp.
dead nettle

 Pachysandra
terminalis Japanese spurge

Tiarella cordifolia foam flower

 Vinca minor
periwinkle

Spring blooming bulbs:

Anemone blanda Grecian windflower

Crocus vernus Dutch crocus

Galanthus nivalis snowdrops

Muscari armeniacum grape hyacinth

Narcissus spp. Daffodils

 Puschkinia
scilloides      striped squill

 Scilla siberica
Siberian squill

for more information on how to best palnt under trees visit

bleeding heart