Macroscopic mechanical properties of materials depend directly on their microstructure. Microscopy, and more specifically tomography, is a key method for studying microstructures. Here, we propose a simple way to use an X-ray tomogram to infer local elastic properties. We distinguish between two scenarios of microstructure images. In the first scenario, the material is composed by very apparent phases so the image can be easily segmented into a set of subspaces with homogenous properties. In the second scenario, the image, as that of sedimentary rocks, contains poorly contrasted phases, including strong intra-phase heterogeneities. For this case, we propose an alternative to segmentation techniques in order to factor in material heterogeneities. To do this, we use the local X-ray attenuation to define elastic moduli. Then, we compute up-scaled elastic moduli by solving the mechanical equilibrium. Finally, we confirm our method by comparing the up-scaled elastic moduli to indentation experiments performed at the same scale.