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The technology of arranging deep foundations using prefabricated piles driven into the foundation by impact or indentation has been widely used in the construction and reconstruction of industrial and civil buildings for a long time. In difficult engineering and geological conditions, the immersion of prefabricated piles must be carried out using preliminary leader drilling. In the presented study, the case of pile driving at a constant speed with the help of leader drilling is considered, since this issue is much less covered in the scientific literature. The main goal is to determine the force that will be required to drive the pile to the depth specified by the project, as well as the subsequent determination of its ability to withstand the design load. At present, the technology for the production of work during pile driving makes it possible to determine the limiting value of the force on the pile at any time. While theoretical methods for studying the interaction between the pile being introduced and the soil mass are not widely used. The present study completely solves the problem of describing the stress-strain state of a soil mass containing a pre-fabricated pile, immersed in the soil by the indentation method using leader drilling. [ABSTRACT FROM AUTHOR]