Seismic hazard assessment can be performed following a neo-deterministic approach (NDSHA), which allows to give a realistic description of the seismic ground motion due to an earthquake of given distance and magnitude. The approach is based on modelling techniques that have been developed from a detailed knowledge of both the seismic source process and the propagation of seismic waves. This permits to define a set of earthquake scenarios and to simulate the associated synthetic signals without having to wait for a strong event to occur. NDSHA can be applied at different geographic scale with different detail levels of modelling. At local scale the source and site characteristics can be take account, whereas at the regional scale seismograms at the nodes of a regular grid are computed. Finite fault simulation is needed to compute realistic ground motions close to a ruptured fault. No reasonable deterministic prediction for many details of a future fault motion can be expected and their variability can be treated in practice only from a statistical viewpoint. Therefore, their effect is simulated through Monte-Carlo approach. To test the accuracy of the method, the L’Aquila earthquake occurred on April 6, 2009 has been modelled. The use of a realistic model for the representation of the extended fault introduces a stochastic element in NDSHA. So the variability due to the stochastic component of seismic source has been evaluated. In standard NDSHA at regional scale, seismograms are computed for an upper frequency content of 1 Hz. The use of a more realistic source model than the scaled point source that takes account of effective duration of rupture process allowed to extend the maximum frequency of computation of seismograms of national scale maps to 10 Hz. A first estimation of uncertainty due to the random representation of the source in national scale maps has been obtained by parametric tests on EU-India Grid infrastructure. NDSHA defines the hazard as the maximum ground motion at the site and it does not supply information about the frequency of occurrence of the expected ground motion. The standard procedure of NDSHA has been modified here, to take into account the additional information of recurrence. The introduction of recurrence estimates in NDSHA allows the generation of ground motion maps for specified return periods that permits a straightforward comparison between the NDSHA and the PSHA maps. Furthermore the map of the recurrence has been associated with standard map of ground motion.