Based on the simplified dynamic model of a bolted flange connection structure with hysteretic buffer, stationary random response of the structure under the transverse load of Gaussian white noise is studied through Monte Carlo simulation. In the simplified model, nonlinear springs with different stiffness of compression and tension are used to simulate the bolted flange connections, and the buffer in the upper part of the structure is modeled as a YarHammond type bilinear hysteretic system. In this case, the rapid calculation of dynamical response for the corresponding cabin of spacecraft structure can be completed by using such simplified model. After nondimensionlization of the equation of motion, probability densities of stationary response are obtained through numerical simulation to reveal the evolution of stationary random response for different values of parameters.