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Three-dimensional and multilayered packets from plates, simulating base-foundation, base-seismoisolator-foundation of constructions, are considered. A general asymptotic solution of three-dimensional dynamic problem of elasticity theory for n-layered packet is built. It is shown that the solution becomes mathematically exact, when entering in the boundary conditions functions are polynomial. The character of the stress-strain state of a three-dimensional packet, when the contact between the layers is complete, is studied in detail. On the base of the mathematically exact solution it is established that when there is a middle layer made of softer material of rubber type, the amplitudes of vibrations on the upper layer decrease sharply. By the same taken the application of seismoisolators is theoretically justified. The analysis of the exact solution of another class of problems, when the contact between the separate layers is incomplete, brought to the conclusion that the tangential displacements informed to the lower layer practically do not influence on the stress-strain states of the above standing layers with complete contact between the layers. The detected phenomena may be applied in the calculations of bases-foundations of constructions in seismosteady building for diminishing the negative influence of the seismic forces.

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