Abstarct: Accurate evaluation of rock mass strength is a key requirement for the successful design and implementation of civil and mining projects. Since rock mass strength is strongly influenced by its discontinuities, investigation of the geometrical and mechanical properties of the discontinuities is important. As the rock mass is composed of natural materials, it is necessary to define the random nature of mechanical properties of the discontinuities, such as its geometrical properties. One of the best ways to simulate the stochastic nature of the geometrical properties of the discontinuities is stochastic Discrete Fracture Network (DFN) modeling. In this thesis, a model is developed to simulate the Potential Discrete Fracture Network (PDFN). In this model, each fracture set may demonstrate different behavior in the applied stress field. Therefore, accurate estimation of the distribution function of failure potentiality of any discontinuity is essential. In this approach, low or high strength discontinuities in rock mass are considered. The main purpose of this study is to estimate the strength of rock mass using the Synthetic Rock Mass model (SRM). This synthetic model consists of a stochastic discrete fracture network model and discrete element model (UDEC) considering fracture potential of the discontinuities. Using the Voronoi algorithm, it is possible to simulate crack growth in rock masses, which can lead to the formation of new rock blocks. In this regard, the cohesive crack model has been coded and used as a constitutive model of Voronoi contact surfaces. Initially, the effect of statistical distribution function usage of the mechanical properties in the discrete fracture network was shown. The used mechanical properties were friction angle, normal and shear stiffness. In comparison with the using distribution function only for the friction angle, using the above three properties results in more rock mass strength dispersion. Then, potential discrete fracture network was presented and statistical distribution function was considered for mechanical and strength parameters of fractures, namely cohesion, friction angle and tensile strength. The results of numerical modeling with potential discrete fracture network indicate the ability of this approach in estimating rock mass strength and different fracture patterns. The reasoning behind, is the fact that the location of assigning values produced by the statistical distribution function in the rock mass varies each time. Therefore, the importance of considering the statistical distribution function for the mechanical parameters of potential fracture network in order to perform and analyze more realistic modeling was demonstrated