Stresses oriented differently often cause azimuthal anisotropy in the effective elastic properties of sedimentary rocks. A quantitative analysis of stress-orientation effects is important to interpret the anisotropic characteristics of mechanical and sonic responses. Brazilian tests are conducted to numerically investigate the stress orientation dependence in complex fractured media. We have developed a consistent workflow of lattice spring models (LSMs) coupled with discrete fracture networks (DFNs). This LSM-DFN model could enable a highly accurate modeling by properly choosing reasonable meshing resolutions, damping values, and strain loading rates. Numerical experiments demonstrate that the angle between the preferred azimuth of cracks and the orientation of the loading stress significantly affect the equivalent elastic moduli. The stress-induced anisotropy of cracked media could be reflected by the tendency of stress-strain responses. LSM-DFN modeling of prestressed cracks has the potential for reconstructing realistic structural attributes and analyzing stress-orientation effects.