The failure strength of rock mass is dominated by mechanical characteristics of rock and geometrical characteristics of joints in the rock mass. Thus, the mechanical characteristics required in a design process for rock mass structures would be the strength of the entire rock mass including joints rather than that of rock material itself although it is in reality impossible to investigate the strength of entire rock mass in site. For this reason we propose a method to evaluate the strength of jointed rock mass considering planes of weakness in terms of a numerical analysis in this study. The proposed method is a multi-scale limit load analysis consisting of two sets of governing equations in macro- and microscopic scales based on a mathematical homogenization method. In macro- microscopic scales, the primal-dual interior point method, which is one of the limit load analyses, is used to obtain the failure load factor of the materials. In addition, the verification of the proposed method is demonstrated by comparison with experiments.