A combined method is developed to determine the cohesion and internal friction angle of a dual-pore-fracture medium and the microstructure-traceless tensor technique describing strength anisotropy of a material, which is further introduced into a three dimensional finite element program. Through the comparison of numerical and analytical solutions for a sample calculation example, the reliability of finite element program developed is validated. The elastoplastic numerical simulations of an assumed rectangular underground cave located in surrounding rock masses cut by three groups of orthogonal fractures are carried out by using Mohr-Coulomb yield criterion, and the states of displacement, stress and plastic zone of surrounding rock masses are analyzed. The computation results show that different distributions and combinations of fracture groups result in varied anisotropies in deformation and strength properties of rock masses, accordingly leading to significant changes in distribution and magnitude of the displacements, stresses and plastic zones in the surrounding rock mass.