This paper proposes one method to analyze the vibration of friction systems with reasonable handling for discontinuities of friction force. That method is applied for multi-degrees of freedom systems and sliding isolation systems. In the case of severe earthquake, it is necessary to consider the pressure variation on the friction surface and contact problems including collision or separation. For those problems, one method is explained in this paper to proceed in numerical integration using stick-slip-contact condition. Several numerical simulations are carried out in the following order. At first, for single mass system subjected to horizontal and vertical earthquake, the effect of frictional sliding isolation is examined. Next, for two-dimensional base isolated structure, the effect of pressure variation and contact problems are investigated. Last, for three-dimensional base isolated structure subjected to tri-axial earthquake, seismic response behavior is shown as an example of analysis for multi-degrees of freedom system.
