Based on the continuing need for crude oil and its products and also the challenges associated with new reservoir discoveries, improving the recovery factor from known oil and gas fields is deemed necessary. Matrix stimulation and hydraulic fracturing (HF) are two common methods for reservoir stimulation, intended to improve the flow connection of the wellbore with the reservoir and therefore aid flow rate and usually enhance the ultimate hydrocarbon recovery factor - RF. HF is usually the most effective approach to accelerate hydrocarbon production and improve RF in many reservoirs as it can access larger reservoir volumes than other methods, particularly in the case of horizontal wells and multistage HF. HF treatment of horizontal drains is a complex engineering process with large capital investment needs; a 16-well shale gas pad in the United States or Canada can cost $USD 100,000,000 or more. Hence, to mitigate risks of inadequate HF treatment by reducing uncertainty in the design phase, HF design parameters may be better defined through laboratory tests. This study was performed on a series of specimens prepared from specimens of core from an Iranian carbonate gas reservoir. The 400 meters cored interval was first categorized into five geomechanical units (GMU) based on rock texture and fabric. Then, six intact specimens from each GMU were selected, and laboratory hydraulic fracturing tests were performed on three specimens of each GMU at three different confining pressures (5, 10 and 15 MPa). The HF test conditions (confining stress, fluid properties, injection rate and etc.) were identical in order to evaluate the lithology variation impacts, and were not intended to assess differences in viscosity, rate, or other related effects. Brazilian tensile strength tests were conducted on three samples of each GMU. By establishing the relationship between breakdown pressures and confining pressures, the HF tensile strength of each GMU was calculated. Results illustrate that there are meaningful differences between tensile strengths inferred from Brazilian tests and those back-calculated from laboratory HF tests. These differences are larger as a function of the porosity: generally, in high porosity specimens, tensile strength values derived from the HF tests are about 4-5 times higher than from the Brazilian test. Issues of defect size and poroelastic effects are invoked to explain the large differences, although proving this quantitatively remains an elusive goal. It is not apparent what mathematical modeling approach might be used to more rigorously assess the differences quantitatively, but a micromechanics fracture modeling approach based on statistical inference using micro- to core-scale tomographic input or digital micro- to macrofabric maps may allow better incorporation of the fabric elements at various scales.