The objective of this thesis studies to implement a method of reconstruction of the X-ray tomography that scanner a large samples with good resolution that would scan inside a cylinder (local tomography) and characterize reals materials. Our method can be done to improve the quantitative and qualitative picture of a ghost. In this thesis, this method is used sue the cellular materials. We conducted tests in situ X-ray tomography on the ERG foam and hollow spheres. A comparison between the results of Finite Element and live testing shows the damage mechanism of these materials.