Abstarct: In recent decades, cutting stone with diamond wire has become one of the most widely used methods in the building stone industry. The cutting rate of stone in the diamond wire method is one of the important criteria in evaluating this method. Many uncontrollable and controllable parameters can affect the cutting efficiency of the stone. Physical and mechanical properties of the stone, operational and instrumental parameters could be mentioned as these effective parameters. In recent years, extensive laboratory and field studies have been conducted on how uncontrollable and controllable parameters effect the cutting rate. Due to the high cost and time of experiments and field studies, numerical models can be of great help in evaluating various parameters on the stone cutting process. Numerical modeling can also be used to investigate a wide range of parameters that are out off the laboratory and technology limits. In this research with using PFC3D software, a numerical model is presented to calculate the cutting rate and analyze the controllable parameters that affecting it, including the peripheral speed of the diamond wire, the number of beads per unit length, pull-back amperage of the machine and the diameter of the beads. Numerical simulation and its validation is baxsed on experiments performed on a granite rock sample. The results of numerical modeling show that the parameters of the peripheral speed of the diamond wire and the pull-back amperage of the machine are directly related to the cutting rate. The optimal value for these parameters is the maximum as possible. In other words, with the advancement of technology and the ability to increase the values of these parameters, higher cutting rates can be achieved. Examination of the number of beads per unit length of diamond cutting wire showed that by increasing it to 36 beads, the cutting rate increases, but with increasing more, the cutting rate remains almost constant. Therefore, this number can be considered as the optimal value for this parameter. Examining the effect of bead diameter on cutting rate, it was concluded that with increasing diameter, the cutting rate would be increased. When bead diameter equals to one centimeter, the cutting rate is maximized. Further increasing of the bead diameter will reduce the cutting rate. Therefore, one centimeter is introduced as the optimal value for bead diameter. By comparing the effect of each of the mentioned parameters on the cutting rate, the pull-back amperage of the machine can be expressed as the most effective parameter on the cutting rate. Finally, with using multivariate regression an experimental relationship between the cutting rate and the studied parameters with a correlation coefficient of 0.974 was presented. This relationship can be used to predict and improve the performance of diamond cutting wire in granite stones.