Hydraulic fracturing is used in the oil industry in order to increase the index of production and processing in the wells whose efficiencies have been dropped due to a long-term harvest or the rocks around the wells are of low permeability. Since the hydraulic fracturing operation is costly, it is of special importance to the project managers to determine the pressure required for hydraulic fracturing and the suitable pump for this operation. The numerical modelings used in this work are aimed to investigate the fracture pressure in the carbonate rocks of Bangestan reservoir in Ahvaz, Iran, and to determine a relationship between the pressure required for fracturing and the confining pressure. In this work, unlike the other ones in this field, the developed numerical models had no initial crack or fracture, and the path of the crack and how the crack grows were studied without any pre-determination and presumption. The results obtained show that, in most cases, the crack starts from the central part of the sample, and is extended to its two ends. The crack extension direction was along the borehole axis inside the sample and perpendicular to the lateral stress. The numerical modeling results were well-consistent with the experimental ones, indicating that the pump capacity constraints in the laboratory could be overcome through numerical modelings.