Kink-bands in rocks have been widely observed in nature and imitated in the laboratory, and the mechanism of their formation has attracted much attention from various researchers for many years. In this paper, a two-phase equilibrium model is presented in which the kink-bands are considered as a high-strain phase and the other regions outside kink-bands as a low-strain phase and the discontinuity of the deformation gradient and stresses is permitted across the interface between those two phases. Based on the present model, we conduct the analysis for the rocks under plane strain compression by finding the minimum value of the compressive loading at which the governing equations have real, physically acceptable solutions. It is revealed that for the rocks with strain-softening behaviour, two-phase equilibrium solutions exist, and the critical value of the compressive loading, the inclination angle of the kink-band, and the stresses and strains inside and outside kink-bands can all be determined by the solution, which are in good agreement with experimental measurements and observations.