In this paper, the determination of equivalent elastic properties of fractured rock masses has been studied using discontinuous numerical method. For this purpose, the discontinuous media of the jointed rock mass with different jointing patterns (including one horizontal joint set, one vertical joint set, two perpendicular horizontal and vertical joint sets, and two non-orthogonal joint sets) were modeled in UDEC software and the induced strain were calculated. Then, the elastic properties of rock mass were calculated by inserting strains obtained from numerical methods into compliance matrixes. In order to verify this procedure, the results of back calculated elastic properties of rock mass from numerical models were compared with those obtained from analytical solutions. Finally, the method of back calculated elastic properties of rock mass from numerical models was applied for confining stress boundary condition (the case without analytical solutions) under different rotation angle of discontinuities and scales. The results of this study show that there is a good consistency between the back calculated elastic properties of rock mass from numerical models and analytical solution; where the relative error is about 4% to 6% for most of the cases. This consistency indicates the accuracy of back calculated elastic properties of rock mass from numerical models and this method can be applied for other cases especially those without analytical solution. Application of this method for rock mass under confining stress (the case without analytical solution) indicates that the elastic properties highly depend to rotation angle.