Acceleration time histories, recorded during the destructive 15 April 1979 (M 7.1) Montenegro earthquake, have been simulated using a stochastic modeling technique for finite faults proposed by Beresnev and Atkinson (1997, 1998a). In this approach, the ground-motion amplitudes are simulated as a summation of stochastic point sources. The length of the fault was taken as 70 km and its width as 25 km, and the fault plane was divided into 13 × 5 elements. The applied methodology is tested against its ability to predict site-specific strong-motion records by the incorporation of mean frequency-dependent site-amplification factors, based on a gross characterization of the site class. The results show that the overall agreement between stochastic and recorded waveforms and spectra is quite satisfying. Nevertheless, significant discrepancies exist at certain stations, implying that site-amplification functions play an important role in the simulation process. A repetition of the simulations combined with the use of site-specific amplification function estimated by the horizontal-to-vertical ratios technique improved the fit to the observed time histories and spectra.