Abstract: Earth penetration in geotechnical engineering is difficult to model, largely due to the transient, cou- pled nature of the impact event. The interaction between the penetrator and the target is inherent due to their vastly different material responses. The loading induced on the penetrator can lead to a significant deformation and potentially high shock levels on any onboard components. It is a challenging task to simulate such problems properly. This paper presents typical progresses, and the principles and features of each simulating method are elaborated. In addition, the rationale of the coupled Eulerian-Lagrangian method is discussed in detail. Two examples, the surface footing and the pile penetration, show that the coupled Eulerian-Lagrangian method is more accurate and convenient than other methods for the penetration analysis in geotechnical engineering. The numerical simulation methods of penetration in geotechnical engineering discussed in this paper can be used by related researchers.