Elasticity of reduced dimension materials remains misunderstood since both experimental and theoretical studies on this subject are difficult to perform. Numerous experiments realised in the early 90's evidenced "elastic anomalies" in small period multilayer systems: "supermodulus", breakdown of the Poisson's effect. The polemic raised by these observations lead us to develop a method to study the elastic constants in thin films on substrates; it combines X-ray diffraction and in situ tensile testing. The results presented in this paper deal with the size effect on the elastic properties in tungsten layers with a thickness of a few nanometers. For that purpose, W/Cu multilayers with various thickness periods A ranging from 3 to 24 run have been analysed.