Earth penetration in geotechnical engineering is difficult to model, due to its transient, coupled nature of the impact event. The interaction between the penetrator and the target is inherently coupled due to the vastly different material response. It is a challenging subject to simulate such problems properly. The traditional finite element method presents difficulties in convergence, unreasonable assumptions and professional interpolation routines. Nevertheless, the coupled Eulerian-Lagrangian method which combines the advantages of Lagrangian and Eulerian method can efficiently resolve the issue. Model tests are carried out to study the behavior of suction caisson jack installed in different types of consolidated soils. The penetration effect on the soil inside the caisson, i.e. soil plugs. is also investigated. The coupled Eulerian-Lagranginan (CEL) finite element method is performed to simulate the experiment process; the results are consistent with test data. The numerical simulating methods of penetration in geotechnical engineering discussed in this paper are accessible for those interested researchers.