We have developed a numerical simulation method for predicting the time dependence (wave form) of pressure at any location in the systemic arterial system in humans. The method uses the matlab-Simulink environment. The input data include explicitly the geometry of the arterial tree, treated up to an arbitrary bifurcation level, and the elastic properties of arteries as well as rheological parameters of blood. Thus, the impact of anatomic details of an individual subject can be studied. The method is applied here to reveal the earliest stages of mechanical reaction of the pressure profiles to sudden local blockages (thromboses or embolisms) of selected arteries. The results obtained with a purely passive model provide reference data indispensable for studies of longer-term effects due to neural and humoral mechanisms. The reliability of the results has been checked by comparison of two available sets of anatomic, elastic, and rheological data involving (i) 55 and (ii) 138 arterial segments. The remaining arteries have been replaced with the appropriate resistive elements. Both models are efficient in predicting an overall shift of pressure, whereas the accuracy of the 55-segment model in reproducing the detailed wave forms and stabilization times turns out dependent on the location of the blockage and the observation point.