The adaptive joining process employing friction-spun joint connectors (FSJC) is a promising method for the realization of adaptable joints and thus for lightweight construction. In addition to experimental investigations, numerical studies are indispensable tools for its development. Therefore, this paper includes an analysis of boundary conditions for the spatial discretization and mesh modeling techniques, the material modeling, the contact and friction modeling, and the thermal boundary conditions for the finite element (FE) modeling of this joining process. For these investigations, two FE models corresponding to the two process steps were set up and compared with the two related processes of friction stir welding and friction drilling. Regarding the spatial discretization, the Lagrangian approach is not sufficient to represent the deformation that occurs. The Johnson-Cook model is well suited as a material model. The modeling of the contact detection and friction are important research subjects. Coulomb’s law of friction is not adequate to account for the complex friction phenomena of the adaptive joining process. The thermal boundary conditions play a decisive role in heat generation and thus in the material flow of the process. It is advisable to use temperature-dependent parameters and to investigate in detail the influence of radiation in the entire process.