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In this paper a model is presented which allows to simulate the dynamic response of a tire rolling over elementary road obstacles, whether its spindle is pinned to a test machine or coupled to a vehicle suspension. First the notion of virtual profile is introduced which allows to decrease the number of degrees of freedom accounted for in the contact area without any significant loss in calculation accuracy. Then the principles of dynamic substructuring methods are discussed and applied for the reduction of complex finite element representations to a limited set of most significant equations. Experimental and predictive methods for the evaluation of tire parameters in the model are reviewed as well as theoretical ways of implementing its coupling to actual suspension models. Finally a set of simulated data is provided under various operating conditions. It is also found that this data shows good agreement with equivlent experimental results.