Hydraulic fracturing in the rock mechanics was including of closing part of the wellbore with packer and increasing the fluid flow in the section of wellbore for induction and propagation of crack in the rock. Hydraulic fracturing process was used in inducing fracture in the oil and gas resources, deep water well and geothermal energy and also determination of in situ stress in the rock mass. In this study, based on the importance of this issue, the fracture condition, crack induction and propagation in the brittle rocks were analyzed. For these reasons laboratory andesite rock samples of Pirtaghi dam site was chosen and then all samples were prepared for laboratory tests. In this research, some rock mechanic laboratory tests such as unconfined compressive strength, tri-axial compressive strength, Brazilian test on the Andesite samples with servo-control instruments with 0.001 (mm/s) loading rate were done. In the next step, fracture toughness of the rock samples using of point load instrument and laboratory hydraulic fracturing tests on the 7 rock sample for estimating induction and propagation of crack under different confining pressure condition were performed. Due to the low strain and the high compressive strength of rock samples; as well as; stress intensity, the energy for propagation of crack in the hydraulic fracturing test was provided in the range of elastic behavior. The results of the hydraulic fracturing tests were shown that crack propagation was grown with high speed owing of geometry of fracture and the value of fracture energy. Also, the failed time of rock samples in the hydraulic fracturing tests, induction and propagation of crack in the low range of time were accepted the previous points. Then the numerical modeling with Abaqus software base on the laboratory condition was done. The geometry and the time of induction and propagation of crack in numerical modeling had a high agreement with laboratory results.