A two degree-of-freedom mathematical model is presented to investigate the friction mechanism of a disc brake system. A contact parameter is introduced to describe the coupling between the in-plane and the out-of-plane motions. The model with the contact parameter is considered under the assumption that the out-of-plane motion depends on the friction force along the in-plane motion. In order to describe the relationship between the friction force and the out-of plane motion, the dynamic friction coefficient is considered as a function of both relative velocity and normal farce. Using this friction law, a contact stiffness matrix along the normal direction can be obtained. The out-of-plane motion is then investigated by both the stability analysis and the numerical analysis for various parametric conditions. The results show that the stiffness parameters of the pad and the disc must be controlled at the same time. Also, the numerical analysis shows the existence of limit cycle caused by the effect of intermittent contact stiffness.