Abstract: Crack interaction is critical to the stability and deformation of rock masses. An accurate and efficient numerical method for solving the crack-crack interacting problem is presented. The method is developed based on dislocation model, stress superposition principle and the Legendre polynomial expansion of the pseudo-traction. It can be used to compute the stress intensity factors of multiple kinked cracks and multiple rows of periodical cracks as well as the overall strains of rock masses containing the multiple cracks under loadings. Many computing examples are given. Numerical results for single faults and crossed faults show that single faults are more unstable than crossed faults. For the problem of multiple rows of periodical cracks, the dependence of the overall strains on the crack configuration and the geometrical and physical parameters is investigated. It is found that the predicted stress-strain curves for rock masses containing single faults are sensitive to the geometrical and physical parameters.