We consider a linear elastic composite medium\ which consists of a homogeneous matrix containing aligned ellipsoidal uncoated or coated inclusions arranged in a doubly periodic array and subjected to inhomogeneous boundary conditions[ The hypothesis of e}ective _eld homogeneity near the inclusions is used[ The general integral equation obtained reduces the analysis of in_nite number of inclusion problems to the analysis of a _nite number of inclusions in some representative volume element "RVE#[ The integral equation is solved by a modi_ed version of the Neumann series^the fast convergence of this method is demonstrated for concrete examples[ The nonlocal macroscopic constitutive equation relating the cell averages of stress and strain is derived in explicit iterative form of an integral equation[ A doubly periodic inclusion _eld in a _nite ply subjected to a stress gradient along the functionally graded direction is considered[ The stresses averaged over the cell are explicitly represented as functions of the boundary conditions[ Finally\ the employed of proposed explicit relations for numerical simulations of tensors descri! bing the local and nonlocal e}ective elastic properties of _nite inclusion plies containing a simple cubic lattice of rigid inclusions and voids are considered[ The local and nonlocal parts of average strains are estimated for inclusion plies of di}erent thickness[ The boundary layers and scale e}ects for e}ective local and nonlocal e}ective properties as well as for average stresses will be revealed[ ร 0888 Elsevier Science Ltd[ All rights reserved[