Friction-induced vibration due to mode coupling is a major concern in a wide variety of mechanical systems. Though there are numerous papers on both linear and non-linear stability analyses of dynamical systems with friction-induced vibrations, the effects of damping on the evolution of the stable–unstable regions is not yet fully understood. The purpose of this work is to study a pin-disc model describing a typical frictioninduced vibration due to a geometric constraint in order to illustrate the effects of damping on linear stability analyses. The results not only illustrate the influence of damping for determining the stable and unstable zones, but they also indicate that the ‘‘most efficient damping factor of the coupling modes'' is an important factor to be taken into account. The physical mechanism causing this change in instability as a consequence of the damping factor is also suggested to help avoid bad design.