The use of the trenchless method of laying underground communications is a profitable alternative to the use of open methods. The method of vibro-impact immersion of steel pipes with an open front end into the ground is widely used. Regular cleaning of the pipe from the formed soil core is one of the most important operations in this technology. The parameters of the soil plug (density, linear dimensions) depend on the physical and mechanical properties of the soil in which the work is performed. The purpose of this article is to establish the parameters for modeling the process of the formation of a soil plug when a pipe is dipped with an open end into a massif, as well as to determine the factors affecting the characteristics of the soil plug. The examples of construction of numerical models of soil massifs when immersing pipes during various technological operations are considered. A computational model of the interaction of the open end of the pipe with the soil mass under loading was constructed for solving by the finite element method in the ANSYS software package. The adopted approach to modeling of formation of a soil plug when the pipe is immersed with an open end into an massif allows to take into account the elastic-plastic properties of the soil, makes it possible to solve the contact problem for the system “surface of the pipe-soil array”. The main limitations and assumptions in modeling the process associated with the amount of computing resources are revealed. The results can be used to build a model of the interaction of the system, as well as in developing a computational model of the process of the combined cleaning of the pipe from the soil core.