YOu can't really plant beneath a cherry tree - as you've discovered, they have a lot of surface roots which often even start appearing above the soil up to 4 feet away. Best to just keep it covered with mulch and plant in pots if you want to plant directly below the canopy.

Thanks Bamboo....I just put a pot there, it looks better now.

You don't say how mature your tree is but I'm guessing over 10 years old. If so well what's growing under my cherry tree may work? (If it isn't a mature tree then ignore all of the below as you will not want give the tree too much competition.)

Heuchera, this will easily grow there once established, I have some growing on bone dry eucalyptus roots so a cherry tree will not be a problem. If there isn't much room between the roots start it off small and it will find it's own room.

Hardy geraniums, I have lots of these too. They will grow on the sunny side and again will find there own route through the roots.

I also have Penstemon 'firebird', Cyclamen, Dicentra.

Then the bulbs... tulips, aliums, narcissus, bluebells.

But 1/4 of the space under mine is Japanese Anemone (you would have to be brave or stupid though because is will mix in with the roots and you will never get it out.) It was here when I arrived and so I had no choice and quite like it but it's getting bigger each year.

All of these are growing under my tree, plus lots more.....but then I don't care if it competes with the tree as it's already too big!

We find violets, primroses, perennial cyclamen, ajuga and lily of the valley do well under our huge cherry tree. Lots of weeds grow really well, too!