The present work involves the development of a new procedure for the generation of synthetic time histories of earthquake ground acceleration. The method is based on a seismological model of the Fourier Amplitude Spectrum of ground acceleration and its Minimum Phase Spectrum. The Minimum Phase Spectrum is selected because it can be computed from the Fourier Amplitude Spectrum. Since the Minimum Phase Spectrum is not an adequate approximation of the Fourier Phase Spectrum of recorded accelerograms, it is modified by means of a cascade of second order all pass filters. To account for the effect of the noise in the Fourier Amplitude Spectrum upon the shape and strong motion duration of accelerograms, the Fourier Amplitude Spectrum of the synthetic time histories is constructed by multiplying the smooth Fourier Amplitude Spectrum given by the seismological model with a noisy function in the frequency domain. The adequacy of the new model is assessed by simulating two well known accelerograms from available seismological data. Also simulated with the new model are ground acceleration time histories caused by the Charleston, South Carolina, earthquake of 1886. As suggested by the simulations, the procedure developed here generates synthetic time histories of ground acceleration with properties similar to those expected from recorded accelerograms. It has the following advantages: (1) it can be used in cases in which no recorded accelerograms are available; (2) it does not require a large computational effort