Understanding the mechanical behavior of nano-structured thin films in relation to their microstructure, in particular to the grain size, is of utmost importance for the development of technological applications. Model nanometric W/Cu multilayers exhibiting different microstructures and supported by a (thin) polyimide substrate are elaborated. The films mechanical response is characterized experimentally by tensile tests carried out in-situ in an X-ray diffractometer installed at a synchrotron beam line. The orientation dependence of elastic strains and stresses is determined by an appropriate micromechanical model accounting for the material microstructure, and based on homogenization schemes. While a good agreement is globally found, the model better reproduces the experimental results of the W component than those of Cu, due probably to the elastic anisotropy of Cu grains. (C) 2007 Elsevier B.V. All rights reserved.