We first give the results of a fully analytical calculation of the strain field associated with the elastic relaxation of a misfitting truncated pyramidal quantum dot (QD) buried in a half space, Assuming linear isotropic elasticity, the displacement field has been calculated in the QD itself and in the matrix for any such inclusion, including the trapezoidal quantum wire (QWR) as a limit. We then show that these calculations are unique in allowing a fast calculation of the strain field of large arrays of elastically interacting QDs or QWRs. We discuss in particular the influence of the neighbouring QDs on the topology and magnitude of the strain field and elastic energy density at the free surface (number, location and depth of potential energy extrema, number of QDs to be included in practical calculations) and the consequences on the stacking of QD multilayers as a function of the shape and depth of the underlying QDs and of the misfit of the new deposit. We finally study analytically the morphological stability of the surface of a half space containing a periodic assembly of embedded QWRs. This leads us to propose an alternative criterion to test the preferred stacking mode in such systems. (C) 2002 Elsevier Science B.V. All rights reserved.