The present paper deals with the passive control of the vibrations of art objects subjected to base excitations. The art object is modelled as a rigid block simply supported on a pedestal which is connected to a visco-elastic device in order to obtain a passive control system. If subjected to seismic excitation, the art object may tilt over the movable supporting mass and eventually overturn, while the sliding is prevented by means of seismic restraints. The nonlinear dynamic equilibrium equations of the structural model for each phase of the motion have been derived for large displacements. The transition conditions between the phases of the motion that may occur have also been defined. Extensive numerical investigations under impulsive and seismic excitations have been carried out in order to both verify the efficiency of the passive control and to evaluate the values of the characteristic parameters of the isolation device which provide the best performance. The results show that the investigated isolation device may be easily and successfully applied for the mitigation of the seismic damage of art objects.