The interlayer relaxation of crystal surfaces and nanocrystals is studied for a number of elements in the Periodic Table by using a tight-binding potential based on the second moment approximation. We find that the extent of relaxation strongly depends on the chemical species of elements and is correlated with the ratio of dimer bond-length to nearest-neighbor distances in solids. The oscillatory behaviour of multilayer relaxation is correlated with large relaxation of the interlayer distance between the first and second layers. (C) 2001 Elsevier Science B.V. All rights reserved.