At present, a vibratory method is used for the construction of prefabricated piles and retaining elements of deep excavations. Especially when building in urban development and difficult geological conditions. The research presented in this paper is devoted to the analysis of the interaction of the pile of friction and a two-layer soil base under a vibrating load on the pile head. An analytical solution of the problem is presented in a static and dynamic formulation. The proposed solution takes into account the elastic, viscous and rheological properties of soils. The pile is considered absolutely not compressible. A similar problem is solved by the finite element method using an elastic-viscoplastic model of soils.
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