The paper considers the dynamic behaviour of the two-layered and multi-layered plate packets under dynamic (seismic) loading. These models correspond to the base-foundation packet structures. The analysis of the various models, including the models of contact between the layers, is derived on the base of the precise solutions of elasticity theory equations. It is shown that the application of the seismoisolator or, in general, less rigid materials between the base and the foundation brings to reduction of the natural frequencies of free vibrations of the packet base-foundation, as well as to the significant reduction of the negative seismic effect on the structures.