Performing Uniaxial Compression Test and Triaxial Compression Tests in rock mechanics play very important role. An alternative method is approved by the International rocks, which was proposed by Kovari at first, known as the Multi-Stage Triaxial Society for Rock Mechanics (ISRM) to determine the mechanical properties of the sufficient quantities or when it is impossible to obtain the required number of Test (MST). Using this method is suggested when samples are not available in samples with almost identical conditions, as well as, when depth of sampling is due to brittle failure. Therefore, in this thesis, it is tried to investigate too high and cost and time consuming are the concerns. On the other hand, in Brittle rocks, multi-stage triaxial test faces with difficulty and obstacles and compare the results of experimental and numerical results with the rock different loading conditions, the following results are obtained. In the failure process during the triaxial tests. Thus, by performing a uniaxial compression test, triaxial compression test, and multi-stage triaxial test on Alamut granite in a laboratory, besides modeling these methods in PFC software in experimental and numerical results for the multi-stage triaxial test i ISRM and Crowford methods was 5% and 3%, laboratory process, the differences between the triaxial compression test and the multi-stage triaxial test in ISRM and Crowford methods were determined to be 4% and 2.5%, respectively. The difference between numerical and laboratory triaxial compression test was about 1%. The differences between the method provides relatively close to the single-stage mode. respectively. The results obtained in this thesis show that although the strength acquired in multi-stage triaxial test in both experimental and numerical modes is less than triaxial test mode, they have reasonable result for quantitative assessment of rock properties. In addition, the Crowford