In the last few decades, many strong earthquakes shacked-up the world. The "Base Isolation System" provides a method to control the seismic response of building structure. The randomness of ground motions and the sensitivity of base isolation buildings to details of the excitation make random vibration analysis necessary. In this paper, the stochastic analysis of base isolated structures which provided with Shape Memory Alloy (SMA), Lead Rubber Bearing (LRB) and Pure-Friction bearing (PF) is studied. The inelastic equations of motion for these structures are derived. Then, they are linearized stochastically to be solved. These linearized equations are solved to obtain the stochastic response of the isolated buildings which compared with that of the fixed base one. It is achieved that the base isolation technique are effective using any type of these isolators.