A method is developed for generating a random process that has the known pertinent properties of recorded strong-motion earthquake accelerograms. The model accelerograms are sections of a stationary, Gaussian, random process with a power spectral density found from the average of the undamped velocity spectra of recorded ground accelerations. Eight pseudo-earthquakes of thirty seconds duration were generated on the digital computer and the velocities, displacements, and velocity spectra were calculated. The average velocity spectra of the real and pseudo-earthquakes correspond closely and the velocities, displacements, and velocity spectra of the real and pseudo-earthquakes exhibit similar statistical behavior. Even some of those features sometimes attributed to the effects of local geology are shown by the pseudo-earthquakes. It is concluded that the artificial earthquakes are satisfactory models of strong-motion earthquakes for the purposes of structural analysis, and that they can be used as standard ground motions for the design of structures. It is proposed to use the pseudo-accelerograms to study the statistics of the responses of hysteretic-type structures to earthquake motion.