In geotechnical engineering the simulation of penetration processes is an important tool for the prediction of the bearing capacity of structures and of the soil behaviour in the near field. Generally the numerical analysis of penetration processes is limited to penetrating bodies, which experience no deformation during simulation. The reason for this limitation is determined by the enormous computational costs. This paper presents a novel method to simulate the penetration process considering the deformation behaviour of slender profiles with relatively low bending and torsional stiffness such as sheet piles. The numerical analyses are carried out using the Coupled Eulerian-Lagrangian (CEL) approach. The modelling method is validated by 1g-model tests. Applying this method to the jacking simulation of sheet piles, in particular U- and Z-sections, it can be shown, that the stress state between the surfaces of web and flange increases due to soil plugging. Hence, higher shaft resistance in the corner regions forces the profile to deform. The influence of the profile's deformation on the reaction forces is significant and must be considered.