Green Leylandii's roots do not usually grow deep, they do however grow out to the sides, so there maybe an issue when planting large trees next to the house.
Our advice is to keep height of those near to a house trimmed to 2 metres (6ft 6ins) or smaller, or simply avoid planting to close.
The best solution is to remove the stump entirely, but if this is not possible you can use caustic soda or a root rotter such as Scotts Roundup Tree Stump & Rootkiller, SBM Job done Tough Tree Stump Killer or Westland Deep Root Ultra Tree Stump & Weedkiller. This is best done in autumn or winter when tree is dormant and sap is not rising, once treated covering the whole top of the stump with a plastic sheet to keep off the rain and secure in place. Children and pets should be excluded from treated areas.
A special thanks to Helen Percy for letting us use her image above, please go to her site to see her story about removing some Leylandii from her garden and many other interesting gardening insights. helenmpercy.com/gardeningblog/2011/02/28/the-most-ambitious-leylandii-removal-yet