The asymptotic method is used to solve the three-dimensional dynamic problem of the elasticity theory on forced vibrations of multi-layered orthotropic plate under full contact conditions between the layers. The analysis of the obtained mathematically exact solutions is conducted and the usage of seismoisolators is proved. For a three-layered packet (foundation-seismoisolator-base) it is shown that in case the layers are rigid enough, the displacements imparted to the lower layer are basically transmitted to the upper layers, and when the middle layer is considerably soft, the amplitudes of the upper layer vibrations are essentially diminishing. The results prove the necessity of using seismic isolators, particularly in the construction of especially responsible buildings, such as schools, hospitals etc., with the aim of decreasing negative influence of earthquakes. The simple algorithm is built in order to calculate the amplitudes of forced vibrations in case of any quantity and configurations of layers. The behavior of the multi-layered packets under various layers configurations is graphically illustrated.