In the transmission systems of vehicles, unforced vibrations can be observed during the sliding phase of clutch engagement. These vibrations are due to frictional forces and may generate noise. Several studies have shown that the stability of such friction systems is highly sensitive to parameters (e.g. friction law, damping) which lead to signicant dispersion. Therefore, uncertain parameters must be considered in the stability analysis of a clutch system. In several studies of the literature, the usual generalized polynomial chaos (PC) expansion has been used to study the stability of a clutch system using nonintrusive techniques. However, non-intrusive techniques require a number of model evaluations (i.e. the computational cost) which can become prohibitive when the studied system has a large number of uncertain parameters. To remedy this problem, in this work, we use the sparse polynomial chaos expansion which has been recently developed in reliability domain. The method is compared to the reference Monte Carlo method and with the usual PC expansion in the context of the stability analysis of a clutch system. The results show that the use of the sparse PC allows a remarkable reduction of the computational cost by ensuring a high accuracy compared with the usual PC expansion.