Uniaxial tensile testing on thin film/kapton composite specimens has been used to determine thin film elastic constants by X-ray diffraction. The method has been applied to a 140-nm-thick tungsten film which is elastically isotropic and to a 560-nm-thick gold film which is elastically anisotropic. The experimental ɛ-vs.-sin2ψ curves are linear for the polycrystalline isotropic tungsten film and nonlinear for the textured gold film. It is shown that a linear analysis of ɛ-vs.-sin2ψ curves allows the direct determination of elastic constants of the tungsten film, while the use of the crystallite-group method is proposed to analyse the nonlinear behaviour of ɛ-vs.-sin2ψ curves of the fibre-textured gold film.