A large shaking table experimental study for a piping system with a friction support has been conducted for many years to investigate the reduction capability of responses of piping system due to frictional effect against earthquake type excitation. Here, we try to evaluate the vibration responses by means of a non-deterministic method, i.e. the statistical equivalent linearization method, for the piping system. The friction forces at a friction support of the piping for modal equations are calculated by means of the statistical linearization method. It has been found that the calculated responses by the linearization method show good agreement with the experimental ones. The equivalent modal damping were also estimated in this process. Seismic performance of the frictional effect is also discussed.