The well known models for the description of the macroscopic elastic behaviour of polycrystalline specimens, as for instance those due to Voigt, Reuss, Neerfeld-Hill and Eshelby-Kroner, predict macroscopic isotropy of the body in the absence of texture, and transverse isotropy when fibre texture is present. A thin film is usually only transversely isotropic, even in the absence of crystallographic texture. A recently re-examined and elaborated alternative model for grain interaction in thin films based on an approach by Vook and Witt is able to predict this transversely isotropic behaviour. An overview of results on the application of the various grain interaction models has been given here: in particular, simulations of X-ray diffraction experiments and calculations of macroscopic elastic constants were performed for untextured and fibre textured thin films of nickel.