Records of strong-motion earthquakes are simulated using a filtered shot noise. Twenty sample records are then used to simulate the response of a structure subjected to earthquake excitation. The stochastic model used to generate the artificial ground acceleration records is designed to produce sample records similar to those of real strong-motion earthquakes of magnitude 8.3 recorded on firm soil at about 45 miles from the epicenter. It is concluded that a filtered shot noise is very suitable for this simulation. An 8-story shear type building with inelastic force-deflection characteristics represented by a bilinear hysteretic model and having various values of stiffness and viscous damping is subjected to twenty samples of the artificial ground acceleration records. Major response parameters are evaluated and Monte-Carlo estimates of the statistics of these parameters are obtained to allow predictions of their values during future earthquakes.