Abstract Many dynamical systems are subject to some form of non-smooth or discontinuous nonlinearity. One eminent example of such a nonlinearity is friction. This is caused by the fact that friction always opposes the direction of movement, thus changing sign when the sliding velocity changes sign. In this paper, a structure with friction-based seismic base isolation is regarded. Seismic base isolation can be employed to decouple a superstructure from the potentially hazardous surrounding ground motion. As a result, the seismic resistance of the superstructure can be improved. In this case study, the base isolation system is composed of linear laminated rubber bearings and viscous dampers and nonlinear friction elements. The nonlinear dynamic modelling of the base-isolated structure with the aid of constraint equations, is elaborated. Furthermore, the influence of the dynamic characteristics of the superstructure and the nonlinear modelling of the isolation system, on the total system’s dynamic response, is examined. Hereto, the effects of various modelling approaches are considered. Furthermore, the dynamic performance of the system is studied in both nonlinear transient and steady-state analyses. It is shown that, next to (and in correlation with) transient analyses, steady-state analyses can provide valuable insight in the discontinuous dynamic behaviour of the system. This case study illustrates the importance and development of nonlinear modelling and nonlinear analysis tools for non-smooth dynamical systems.