Characterizing the elastic properties of rocks is a key parameter in reservoir engineering. However, these natural materials exhibit a wide variety of microstructures, even if they belong to the same facies, leading to a significant dispersion of their elastic properties. The evolution of the Young's modulus of seven carbonate rocks as a function of their global porosity shows that porosity is not the only factor controlling the elastic properties. The purpose of this study is to understand which microstructural parameters impact the rock elastic properties. A full procedure has been developed to combine nanoindentation measurements with Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS), in order to identify the volume fraction and elastic properties of the mineral phases of each rock. After performing nanoindentation grids on the samples, SEM-EDS analyses were carried out in ex-situ conditions. A specific method was needed to identify the locations of the shallow imprints in the microscope, so that a mineral phase can be attributed to each indentation test (Figure 1). EDS mapping of the whole surface of the samples was also performed to get a statistically representative characterization of the mineralogical composition, and Mercury Intrusion Porosimetry tests were carried out to assess the pore size distribution and evaluate the volume fractions of the porosity families.