In accordance with the random vibration theory

the statistical probabilistic characteristics about the maximum displacement response between layers of parallel base isolated structure

are analyzed; the calculating formula of displacement mean value and standard variation value are derived. With a 4-story parallel base isolated RC frame chosen as numerical example，the results of the mean and standard variation responses of the maximum inter-story drift are gained. It indicates that the maximum displacement mean value of the isolation layer will reduce if the fundamental frequency ratio of base isolation system to the fixed base system and the yielding force of the isolation layer are increased.