Most of the base isolated buildings or structures are built on laminated rubber bearings in order to give them certain natural periods. This situation, however, also encourages structural engineers to research and develop nonrubber-type isolation systems such as linear motion bearing isolators and friction pendulum systems. It is considered that the nonrubber-type isolation systems can be applied to important industrial facilities, such as LNG tanks, boiler facilities, and so on, to refine their seismic reliabilities. This device of a nonrubber-type isolation system uses the energy loss associated with sliding to reduce the deleterious effects of earthquakes. However, when using nonrubber-type isolation systems with sliding in the atmosphere, long term durability of the systems must be taken into account. It may be difficult to maintain the friction coefficient of the system. In this paper, a stochastic study of the effect on rotational motion and isolation performance of two structures subjected to an earthquake with a friction pendulum bearing is analyzed with a Monte Carlo method.