Carrier pile is newly developed in recent years. It utilizes a column hammer to tamp the filling in the deep soil, which forms an expanded carried at the pile end. This will greatly increase the vertical pile bearing capacity. Although the carrier pile has been widely used in practice, rare theoretical analysis has been conducted to check the size of the reinforced area and the compaction effect. This greatly restricts the popularization and development of the carrier pile. Under this condition, the process of the tamping through a column hammer is simplified as the spherical cavity expansion model. The soft clay is described by the MCC model. Then, a series of partial differential equations (PDEs) for spherical cavity expansion is constructed. Similarity solution technique is used to transform the PDEs to ordinary differential equations (ODEs), which can be numerically solved through the ODE solver. Subsequently, a series of parametric analyses were conducted to investigate the variation of the soil strength and stiffness after spherical cavity expansion and the size of the compaction zone. This reveals the reinforced mechanism of the formation of the carried part of the pile from the theoretical viewpoint and provides a theoretical basis for constructing the theoretical calculation methods for the vertical bearing capacity of the carrier pile considering the compaction effect.