Friction-induced vibration due to mode coupling is a major concern in a wide variety of mechani cal systems. Stability analysis and the associated non-linear amplitudes around a steady-state equilibrium point actually are two of the most important points in the study of non-linear dynamical systems de­ pending on given control parameters. Determining stable and unstable regions is only one aspect of the problem of friction-induced ftutter instability. The instability magni tude is a more significant design factor than the instability region. In this paper, we propose to apply interval analysis to obtain the ma.ximum and minimum amplitudes of a complete non-linear mechanical system. This approach allows us to avoid numerical procedures that are both time and cast consuming to perform when parametric design studies are needed.