The main aim of this study is to examine on the real and simulated earthquakes effects. This paper deals with the use of ARMA models in earthquake engineering. The time-varying auto regressive moving average (ARMA) process is used as a simple yet efficient method for simulating earthquake ground motions. This model is capable of reproducing the nonstationary amplitude as well as the frequency content of the earthquake ground accelerations. The moving time-window technique is applied to synthesize the near field earthquakes, Chlef-1, Chlef-2, Chlef-3 and Attaf 1980 recorded on dense soils in Algeria. This model, is based on a low-order, time-invariant ARMA process excited by Gaussian white noise and amplitude modulated using a simple envelope function to account for the non-stationary characteristics. This simple model gives a reasonable fit to the observed ground motion. It is shown that the selected ARMA (2,1) model and the algorithm used for generating the accelerograms are able to preserve the features of the real earthquake records with different frequency content. In this evaluation, the linear and non linear responses of a given soil layer have been adopted. This study suggests the ability to characterize the earthquake by a minimum number of parameters.