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Analysis of the stability of slopes in fractured rock masses is not trivial and is fraught with uncertainty and risk. A DFN-DEC model (Discrete Fracture Network-Distinct Element Code) based on the MATLAB platform is developed to evaluate the stability of rock slopes with random fractures. Then, the influences of mean values of geometric characteristics (i.e., the trace length T, the dip D, and the spacing S) for both the horizontal (denoted with 1) and inclined (denoted with 2) fractures on the mean slope stability are investigated. The results indicate that the proposed DFN-DEC model based on the MATLAB platform is adequate, robust, and can generate more realistic fracture networks. By means of probabilistic analysis (i.e., Monte Carlo simulation), we can obtain a more accurate stability assessment result of fractured rock slopes. In addition, it is found that the ${\mu }_{Fs}$ (the mean of Fs) of slopes decreases with the increase in ${\mu }_{T_1}$, ${\mu }_{T_2}$ (the mean trace length of horizontal and inclined fractures, respectively) and ${\mu }_{D_1}$ (the mean dip of horizontal fractures), and increases gradually with the increase in ${\mu }_{D_2}$ (the mean dip of inclined fractures), ${\mu }_{S_1}$ and ${\mu }_{S_2}$ (the mean spacing of horizontal and inclined fractures, respectively). Furthermore, the geometric characteristics related to inclined fractures have a much greater influence on ${\mu }_{FS}$ than that related to horizontal fractures. This study can be well applied in engineering practice, e.g., preliminary evaluation of the slope stability according to the statistics of fracture geometric characteristics. Full article