A simulation of the lateral ground motion of strong earthquakes is performed with the use of a random function generator and an analog computer. The statistical properties of the simulated earthquake are similar to those of actual earthquakes. The simulation is then used as the excitation applied to a structural system, which is also modeled on the analog computer. The statistical behavior of the magnitude of the peak response of the structure is established using a basic Monte Carlo technique with several simulations of the earthquake and associated structural response. The analog computer has the advantage over the digital computer in that several simulations can be performed in a relatively short period of time. The Gumbel Type I distribution of maxima is used to describe the distribution of responses. The experimentally determined statistical parameters relate directly to the seismic safety of a structure. In addition, a study of the seismiic reliability of the bilinear hardening system is given as an example.