The Roman travertine is an ornamental rock, historically present in Roman architecture, which even in present days is much used in decorations and facades. However in the scientific community it is considered a rock similar to carbonate reservoirs, especially the Brazilian pre-salt. The present work sought to carry out an experimental study of the Roman travertine, focusing on the anisotropic geomechanical behavior in two directions (normal and parallel to the sedimentary bedding) under tension values consistent with those occurring in reservoirs. For this, several macro and microscopic analyzes were carried out, including high resolution electron microscopy in order to study the properties of travertine and its porous structure. Chemical analysis of the material and laboratory measurement of the most varied parameters to obtain a satisfactory list of index properties aided in this context. Complementary strength tests, such as the point load test and indirect tensile strength test (Brazilian Test) enriched the study with results of rupture in the directions perpendicular and parallel to the bedding. Finally, it was studied the anisotropic geomechanical behavior under normal and parallel optics to the sedimentary bedding through triaxial tests with confining stress ranging from zero (uniaxial) to 40 MPa, this interval very close to the effective stresses from Brazilian carbonate reservoirs. Due to the great heterogeneity, the specimens were separated into groups with similar total porosity ranges. Then, with results of stress-strain plots and stress trajectories, several comparisons were possible in terms of geomechanical behavior and observe that not always the increase of the confining stress and the lower porosity will result in greater mechanical resistance.