High-pressure water jets are widely used in various industries for cutting various types of metal, wood, paper, concrete and stone materials. In this research, the stone cutting process by high-pressure water jets has been simulated using numerical modeling with the aim of determining the optimal parameters and improving the efficiency of the stone cutting process. In the numerical model, abrasive particles along with the pressurized water flow exit the water jet nozzle at high speed and cut the stone elements. The stone cutting process by water jets has been simulated using the finite element method of fluid particle hydrodynamics in the LS-DYNA software. The effect of the parameters of speed, dwell time, volumetric concentration and diameter of abrasive particles on the depth and volume of stone cutting has been investigated. The results show that with increasing the water jet velocity, the depth and volume of stone cutting increase. With increasing the dwell time of the water jet on the stone, more energy is spent on cutting, which leads to an increase in the depth and volume of stone cutting. Also, by increasing the volumetric concentration of abrasive particles to 4%, the depth and volume of stone cutting increase with a gentle slope, but after that, no significant improvement is observed in increasing the depth and volume of cutting. By increasing the diameter of abrasive particles to 1 mm, the depth and volume of stone cutting also increase, but after that, the depth and volume of cutting remain constant or decrease. Therefore, in order to improve the cutting quality of the stone studied in this research, along with other assumptions, a volumetric concentration of abrasive particles of about 4% and a diameter of abrasive particles of about 1 mm are recommended.