The broad variety of pile types and fabrication methods, depending on the pile-soil interaction mode, include either soil extraction or soil displacement. Although piles are applied everywhere, the current foundation engineering practice faces many issues of pile bearing capacity evaluation. As compared with precise but expensive in-situ methods that require special equipment, the methods for pile bearing capacity analysis do not demonstrate adequate compatibility with real data, especially for soil displacement piles. The engineering method [1] based on correlations of design resistances and soil physical properties is far from perfect either. This paper presents an analytical model for pile installation into a leader hole. The authors did their best to make the model valid so that the model input parameters and relationships would be a part of the on-site geological survey report. The known pile analysis techniques consider a pile as just being in soil with no data on how the pile got there and what changes in the soil characteristics could happen. Therefore, it is necessary to develop an analytical model for a rigid pile forced into a plastically compactable soil. Among current publications on the analysis of pile (probe) penetration into soil, the paper by Fedorovsky and Grevtsev [2] should be mentioned. The present paper employs axisymmetric solutions, which are realistic due to the following facts. Firstly, the symmetry does not consider the issue of stress and strain incompatibility in the case of complex loading. Secondly, the actual velocity fields can be simulated by kinematically admissible fields of horizontal velocities that define the powers of internal forces; this assumption is realistic and enables allocation of the upper bearing capacity boundary according to the Gvozdev theorem. Finally, the mathematical problem reduces to a simple solution of just one nonlinear first-order differential equation. As in many other methods, including the practical one included in Russian construction codes, the authors solved two problems: one for the pile tip and another one for its lateral surface. When analyzing driven pile bearing capacity, a dynamic method based on the energy conservation law is often applicable. The bearing capacity so evaluated appears to be close to the actual one, which demonstrates the adequacy of the applied method. However, the dynamic method of pile bearing capacity analysis requires pile dynamics test data. In order to solve the first problem, the volume conservation law was applied, i.e., the pile volume in the soil was assumed to be equal to the reduction of the total pore volume around the pile. We neglect the complicated soil compaction phenomena around the pile tip during the pile driving and assume that the soil around the pile is compacted in the radial direction alone.