AbstractDigital Rock physics is a numerical framework applying image‐based methods to determine effective material properties of rock. It is possible to find several of these methods in the literature, but we focused mainly in micro X‐Ray Computed Tomography (µXRCT) to acquire the digital rock samples. After scanning the 3‐D microstructure, morphological filters and numerical simulations were performed to characterize the samples. In particular carbonate rocks present a mismatch in numerical results compared to laboratory experiments. The elastic parameters, the P‐ and S‐wave moduli, respectively,are overestimated when compared to ultrasonic measurements in the laboratory. We describe possible causes of this mismatch and propose a new segmentation technique to improve the correlation between numerical simulations and laboratory data. Furthermore, the workflow proposed for the characterization of carbonate rocks has been applied to different digitized samples from different sources, and a data driven material law has been found that fits better experimental results than the lower Hashin‐Shtrikman bound. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)