The main aim of the present work consists in the validation of stochastic method for simulating weak ground motion in a diffusive regime due to low-to-moderate magnitude earthquakes, and in particular in its application to a volcanic area. We simulated the peak ground acceleration and the response acceleration spectra caused by two earthquakes scenarios (MD 4.3 and MD 5.4) at Mt. Vesuvius volcanic area by using the stochastic finite-fault simulation method. We validated the stochastic methodology by combining source, path, and site parameters of the investigated area considering the time duration parameter, Trms, calculated on the study seismograms. The values of time durations are confirmed by calculating the same parameter, Trms, on the seismogram energy envelope described by multiple scattering models, in terms of scattering and the intrinsic dissipation coefficient. Initially, the simulations were evaluated for 10 local earthquakes (1.7≤MD≤3.6) that occurred at Mt. Vesuvius in 1999 and are then compared with the observed data. The comparison between simulated and observed seismograms has been used to calibrate the stochastic procedure, and has been considered as the starting point for simulating ground motion for the scenario earthquake (MD>3.6) that could occur in the study area. The scenario earthquake and the relative fault features were chosen on the base of statistical, tectonic, structural, and historical studies of the study area. We simulated ground motions for a maximum-magnitude value, Mmax, of 4.3, determined from examination of the Gutenberg–Richter law for the study area, and also for an Mmax 5.4, a magnitude that is associated with the earthquakes that struck the ancient town of Pompei 17 yr before the eruption of Mt. Vesuvius that occurred in A.D. 79. The largest values of Amax for the MD 4.3 seismic event are in the range of 0.140g–0.029g. In the case of MD 5.4, we obtain peak ground acceleration values in the range between 0.17g and 0.55g.