In this paper, we propose a method that evaluates the strength of rock structures. The method consists of a classical limit load analysis in plasticity theory and a homogenization method. The homogenization method gives macroscopic stiffness of rock mass from the distribution of cracks and mechanical properties of intact rocks. The macroscopic failure criterion of the mass is also given by numerical analyses based on the homogenization method. The failure strength of a rock mass structure is reasonably evaluated by limit load analysis in a form of Linear Programming.