In the present paper is shown the influence on the local seismic response analysis exerted by considering dispersion and uncertainty in the seismic input as well as in the dynamic properties of soils. In a first attempt a 1D numerical model is developed accounting for both the aleatory nature of the input motion and the stochastic variability of the dynamic properties of soils. The seismic input is introduced in a non‐conventional way through a power spectral density, for which an elastic response spectrum, derived—for instance—by a conventional seismic hazard analysis, is required with an appropriate level of reliability. The uncertainty in the geotechnical properties of soils are instead investigated through a well known simulation technique (Monte Carlo method) for the construction of statistical ensembles. The result of a conventional local seismic response analysis given by a deterministic elastic response spectrum is replaced, in our approach, by a set of statistical elastic response spectra, each one characterized by an appropriate level of probability to be reached or exceeded. The analyses have been carried out for a well documented real case‐study. Lastly, we anticipate a 2D numerical analysis to investigate also the spatial variability of soil's properties.