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The passage of trams in urban areas is a source of cyclic vibration which can induce damages in buildings close to the track. This aspect is even more relevant in the case of historical buildings and monuments because of their intrinsic fragility and the importance of preserving them as unaltered as possible for the next generations. In this framework, the purpose of this paper is the development of a mathematical modelling, based on experimental measurements, for the numerical simulation of vibration due to tram passages close to the so-called temple of Minerva Medica in Rome. The vibration signals were recorded at some points on ground level and on the structure by the use of GPS synchronized seismographs equipped with triaxial velocimeters. By means of spectral analysis of the acquired data, time windows associated to each tram passage have been assumed as stochastic nonstationary processes characterized in terms of energy and dominant frequencies by an evolutionary power spectral density. The signals acquired at different points due to the same passage define a multivariate process. The model would like to allow the simulation of the input at the base of the monument and the evaluation, through finite element analysis, of the exposure of the structure to cyclic stresses under different amplitudes highlighting the probability and location of damages in time.