We used the stochastic method proposed by Beresnev and Atkinson (1997, 1998a) for finite faults to model the 30 September 1999 Mw 7.5 Oaxaca, Mexico earthquake. This large intraplate event was located close to the coast and caused important damage in the state of Oaxaca. We modeled acceleration records from 10 strong-motion stations located near the rupture and at regional distances. The site response of the stations used was determined using more than 100 additional records from other events recorded at the sites of interest. We estimated average spectral ratios between horizontal and vertical components of ground motion (hvsr method), and we incorporated the site response estimates in the stochastic simulations. We also analyzed the decay of the observed spectral amplitudes with hypocentral distance and estimated the attenuation relation to be Qs = 416.5 f0.7. The main event had a normal-faulting mechanism with a fault plane 90 km long and 45 km wide. We divided the fault plane into 9 × 5 subfaults to apply the point-source formalism. Specific slip weights were prescribed on the individual subfaults using the slip distribution obtained by Hernandez et al. (2001). Then, we looked for values of the radiation-strength factor (sfact) and the stress parameter (σ) that gave the minimum model bias of the acceleration response spectra. We found that sfact = 1 and σ = 90 bars provided the best fit to the observed response spectra and peak ground acceleration (pga). These results will be useful to estimate the regional pga generated by earthquakes with similar source characteristics as the 30 September 1999 event.