A statistical study has been done to investigate (i) the variation of spectral responses of structures due to artificially generated earthquake records with identical statistical properties, (ii) the effect of duration of strong shaking phase of artificial earthquakes on the response of structures, and (iii) the number of earthquake records needed for time-history response analysis of a structure in a seismic region. The results indicate that the flexible structures are more sensitive to the inherent statistical variations among statistically identical earthquake records. Consequently several records must be used for time-history response analysis. A sample of eight or more records appear to provide a good estimate of mean maximum response. The duration of strong shaking can significantly affect the maximum response. Based on the results, it is suggested that for the purpose of estimating peak response, the strong shaking duration of the input earthquake motion should be at least four times the natural period of the structure. The maximum responses due to statistically identical ground motion records are observed to fit approximately the type 1 extreme value distribution. Thus, it is rationally possible to choose a design value based on the mean, standard deviation of the spectral response values and tolerable probability of exceedance.