A study of the application of seismic isolation system have been widely researched in order to increase the safety of seismic analysis for nuclear power plant(NPP). In the design of base isolated NPPs, the seismic analysis of interface piping system multi-supported between base-isolated and fixed building is one of the key issues. For the seismic design of interface piping system, it is needed not only rigidity to withstand the force of the inertia response generated by excitations from base-isolated and fixed building but also flexibility to cope with the large relative displacements between two buildings. In order to meet seismic requirements of interface piping system, this paper utilized two methods to perform the seismic analysis of MS interface piping system. First, in order to satisfy the rigidity requirement of MS interface piping system, this paper adapts Multiple Input Response Spectrum (MIRS) method together with the SRSS combination between support groups, USNRC Regulatory Guide 1.61 damping as seismic analysis method to consider different vibration characteristics of base-isolated and fixed building. Second, in order to secure the flexibility of MS interface piping system, this paper use the method to adjust the stiffness of pipe supports installed on MS interface piping system, and performs the sensitivity study on the stiffness of pipe support to find the optimal stiffness that can distribute the excessive piping stress and support loads occurred in the local portion of MS interface piping system.