Though many models for the simulation of earthquake records have been suggested, they are either unrealistic or restricted to a qualitative simulation. If the basic mechanism of earthquakes at different places is similar the underlying mathematical pattern of the different recordings may also be alike. Due to the complexities involved in analyzing the fundamental mechanism, a search for the common pattern must be carried out among the few available ground acceleration records. An attempt has been made in this paper in this direction. An analysis of past records shows that the strength of the oscillations exhibited by the number of zero crossings and extremes in a given interval and the nonstationary random nature revealed by the time-dependent variance function are important characteristics. Using this information a stationary random process modulated by a deterministic function has been developed. Almost all types of known records can be generated from this model by varying its parameters. Approximate methods have also been developed for estimating these parameters in artificial simulation. To test the model, ensembles of a single pulse, a ten-second, a thirty-second and a very long record have been simulated and analyzed for relative velocity and time response spectra. Many quantities realized in the records compare well with the corresponding ones fixed beforehand. Suggestions are made for using the model in aseismic design.