This paper presents results obtained using three numerical approaches for the basal heave analysis of a hypothetical circular shaft: the Finite Element Method (FEM), Numerical Limit Analysis (NLA), and the Material Point Method (MPM). The Strength Reduction Factor (SRF) methodology was used in conjunction with the MPM, NLA, and FEM to analyze the stability of this structure under dry and saturated conditions. In this paper, we introduced a methodology for applying the SRF technique within the framework of the MPM in a three-dimensional (3D) context. The paper compares and discusses results from the three analysis methods concerning the factor of safety and failure mechanisms. In particular, the failure surface and the run-out condition were also evaluated for a hypothetical case with large deformations using MPM. The results obtained from the three numerical methods exhibited good consistency. Regarding FEM, NLA required the least computational cost to get the safety factor, being a more appealing tool for its estimation, and the MPM allowed consideration of large deformations in the simulations without any additional numerical treatments like remeshing. The current work demonstrates a potential strategy for combining MPM, NLA, and FEM approaches to determine the failure mechanism and the post-rupture processes with large deformations.