A system of stacked rigid blocks can be found in many applications of non-structural components: a statue resting on the top of a table is such an example. Previous studies usually assume that the friction at contact interface is so large that only rocking motion can be activated. However, this assumption may not be realistic when assessing the seismic response of unanchored non-structural components. Motivated from this constraint, this paper contributes to the state-of-the-art research of the classical rocking problem by presenting a numerical model within which sliding, rocking and sliding-rocking response of stacked rigid blocks can be computed by the time-history analysis. The exact fully nonlinear equations of motion, transition criteria for different response modes and treatment to handle the impact are presented in detail. The accuracy of the developed model is validated. A case study is also provided to investigate the overall failure probability of the stacked rigid blocks with realistic friction coefficient. In this particular case study, it is also shown that increasing the friction coefficient makes the stacked rigid blocks more susceptible to failure.