Carbonate reservoirs contain between 50 and 60 percent of oil and gas reserves in the world. However, these rocks have presented considerable operating problems during the phases of drilling and production. Such problems are originated by the difficulties in the proper characterization of these rocks due to the complex spatial distribution of its micro and macro structure. While both scales have importance on the carbonate behavior understanding, this paper deals with the analysis of the microstructure. In this context, the aim of this work is part of the processing and digital image analysis, mesh preparation and finite element numerical simulation to predict elastic properties, in order to correlate the microstructure and the Young s modulus. Using digital images of outcrop samples (travertine) considered as possible analogous to carbonate rocks reservoir. The methodology implemented afforded sub-samples that include a range of porosities and microstructures for a single sample well numerically simulate the Young s modulus. It is concluded in this study that the larger pores (vuggys) are mainly responsible for the behavior of the material when it is loaded, and also the influence of the porous structure in the results, it was observed that the position of pores affects the modulus of elasticity of sample.