Abstarct: Precise estimation of rock mass strength is one of the main requirements for planning and implementing civil and mining projects in the rock. Nowadays, numerical modeling is increasingly put forward as a method of determining the strength of the rock mass. The most important step in the numerical modeling of rock masses is to accurately define the rock mass joints network (designing a geometrical model of the joints network). The goal of this research is to estimate the strength of a rock mass with non-persistence joints using Synthetic Rock Mass (SRM) model consistence of 3-D Stochastic Discrete Fractures Network (DFN) and discrete element method PFC3D. For this purpose, the geometric-stochastic joint network model and a computer code, named DFN-FRAC3D, written in C++, has been developed, considering the statistical characteristics of joint size baxsed on Veneziano. The DFN-FRAC3D has the most features of commercial software and computer programs that have been developed up to this date. Modeling joints patterns related to faults and also random sampling with the different number and sizes in the large DFN are a unique feature of the DFN-FRAC3D. To evaluate the strength of jointed rock masses, at the beginning, the three-dimensional geometric model of joint network has been prepared using surveyed data in the Access Tunnel of Rudbar Lorestan Dam & Hydropower Plant and the best probability distribution functions fitted on geometric characteristics of existing joint sets in this region. The prepared geometric model, statistically showed good agreement with the actual rock mass in the region. Then, the smallest dimension of the prepared geometric model in which the maximum number of joints can contribute to reduce the rock mass strength (Representative Elementary Volume (REV)) is determined by using SRM model and proposed accurate approach in this thesis. baxsed on the remaining constant of average strength, decrease of coefficient variation of strength and decrease of the ratio of average persistence to size of the block (relative persistence), the strength REV of the considered rock mass is estimated equal to 7m×7m×14m. The average strength of the studied rock mass is 8 MPa. This value is approximately 45% of the intact UCS. Finally, the relationship between the strength and the statistical parameters of the geometric properties of the joints network was evaluated in determined REV size. In this step, the smallest possible model which is a representative of a large rock mass and contains the statistical properties of the rock mass with an allowable error (Statistical REV (SREV)) is defined. It was found that SREV is a block with dimensions of 7m×7m×14m where volume intensity of joint is equal to large block of DFN and the empirical cumulative distribution function of the joint persistence has a maximum allowable difference 1.15 in comparison with the large block of DFN.